LCM of 1,999,999,970 and 399,999,981, the Least (Lowest) Common Multiple Calculator. LCD, The Lowest Common Denominator. Find More Multiples Starting From LCM

Calculator of the LCM of 1,999,999,970 and 399,999,981, the least (lowest) common multiple of the numbers. The common denominator. More multiples

What is the least common multiple (LCM)?

  • The least common multiple (LCM) of two numbers is the smallest non zero natural number that is a multiple of both numbers.
  • For example, the LCM of 2 and 3 is 6.
  • You will see below how it is calculated by two methods.

  • Other multiples of two numbers

  • Once you have calculated the LCM of two numbers, you can find other multiples of these two numbers by multiplying LCM by any other natural number.
  • For example, the LCM of 2 and 3 = 6, then the following numbers are also multiples of the numbers 2 and 3: 6 × 0 = 0; 6 × 2 = 12; 6 × 3 = 18; ... and so on.
  • There are infinitely many multiples of any two numbers.

  • The common denominator of two fractions

  • Calculating the common denominator of two fractions is equivalent to calculating the lowest common multiple (LCM) of their denominators.
  • By example: in order to add two fractions, 1/2 and 1/3, we need them to have the same denominator, preferable as small as possible. Well, this common denominator is 6, the least common multiple of 2 and 3: 1/2 + 1/3 = (3 × 1) / 6 + (2 × 1) / 6 = 3/6 + 2/6 = 5/6
  • » Calculator for adding fractions
  • » Calculator for subtracting fractions
  • » Calculator for comparing fractions

lcm (1,999,999,970; 399,999,981) = ?

Used methods: 1. The prime factorization of numbers. 2. The Euclidean Algorithm

Method 1. The prime factorization:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


1,999,999,970 = 2 × 5 × 743 × 269,179
1,999,999,970 is not a prime number but a composite one.

399,999,981 = 3 × 133,333,327
399,999,981 is not a prime number but a composite one.



Calculate the least common multiple, lcm:

Multiply all the prime factors of the two numbers. If there are common prime factors then only the ones with the largest exponents are taken (the largest powers).


The least common multiple:
lcm (1,999,999,970; 399,999,981) = 2 × 3 × 5 × 743 × 269,179 × 133,333,327 = 799,999,950,000,000,570
The two numbers have no prime factors in common
799,999,950,000,000,570 = 1,999,999,970 × 399,999,981

Method 2. The Euclidean Algorithm:

1. Calculate the greatest (highest) common factor (divisor):

  • This algorithm involves the process of dividing numbers and calculating the remainders.
  • 'a' and 'b' are the two natural numbers, 'a' >= 'b'.
  • Divide 'a' by 'b' and get the remainder of the operation, 'r'.
  • If 'r' = 0, STOP. 'b' = the gcf (hcf, gcd) of 'a' and 'b'.
  • Else: Replace ('a' by 'b') and ('b' by 'r'). Return to the step above.


Step 1. Divide the larger number by the smaller one:
1,999,999,970 ÷ 399,999,981 = 5 + 65
Step 2. Divide the smaller number by the above operation's remainder:
399,999,981 ÷ 65 = 6,153,845 + 56
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
65 ÷ 56 = 1 + 9
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
56 ÷ 9 = 6 + 2
Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
9 ÷ 2 = 4 + 1
Step 6. Divide the remainder of the step 4 by the remainder of the step 5:
2 ÷ 1 = 2 + 0
At this step, the remainder is zero, so we stop:
1 is the number we were looking for - the last non-zero remainder.
This is the greatest (highest) common factor (divisor).

The greatest (highest) common factor (divisor):
gcf, hcf, gcd (1,999,999,970; 399,999,981) = 1


2. Calculate the least common multiple:

The least common multiple, Formula:

lcm (a; b) = (a × b) / gcf, hcf, gcd (a; b)


lcm (1,999,999,970; 399,999,981) =

(1,999,999,970 × 399,999,981) / gcf, hcf, gcd (1,999,999,970; 399,999,981) =

799,999,950,000,000,570 / 1 =

799,999,950,000,000,570


» The Euclidean Algorithm


The least common multiple:
lcm (1,999,999,970; 399,999,981) = 799,999,950,000,000,570 = 2 × 3 × 5 × 743 × 269,179 × 133,333,327

Scroll down for finding more multiples...

More multiples starting from the least common multiple

  • Any common multiple of two numbers is also a multiple of the least common multiple, LCM, of twose two numbers.
  • The following numbers are also multiples of 1,999,999,970 and 399,999,981:
    799,999,950,000,000,570 × 0 = 0 ... 799,999,950,000,000,570 × 2 = 1,599,999,900,000,001,140 ... 799,999,950,000,000,570 × 3 = 2,399,999,850,000,001,710 ...
  • There are infinitely many multiples of any two numbers..

How to check if a number is a common multiple of two numbers?

  • After calculating the LCM, divide the number to be checked by the LCM. If the remainder of this division is zero, then the number being checked is a multiple of the other two numbers. If the remainder is not zero, then the number being checked is not a multiple.
  • For example: the LCM of the numbers 4 and 6 is 2 × 2 × 3 = 12.
  • Question: is 36 a multiple of the numbers 4 and 6? Answer: 36 ÷ 12 = 3 and the remainder is 0, so 36 is a multiple of 4 and 6.
  • Question: is 28 a multiple of the numbers 4 and 6? Answer: 28 ÷ 12 = 2 and the remainder is 4, so 28 is not a multiple of 4 and 6.

Why is it useful to calculate the least common multiple?

  • In order to add, subtract or sort fractions with different denominators, we must make their denominators the same. An easy way is to calculate the least common multiple of all the denominators (the least common denominator).
  • By definition, the least common multiple of two numbers is the smallest natural number that is: (1) greater than 0 and (2) a multiple of both numbers.


Similar operations, the least (lowest) common multiple, LCM, calculations:

» LCM of 2,000,000,008 and 400,000,026, the Least (Lowest) Common Multiple Calculator. LCD, The Lowest Common Denominator

» Monthly Calculations: Values of the Least (the Lowest) Common Multiple, LCM

» Month 11, 2025 [November]: Monthly Calculations: Values of the Least (the Lowest) Common Multiple, LCM


Share

The least common multiple (lcm). What it is and how to calculate it.

  • The number 60 is a common multiple of the numbers 6 and 15 because 60 is a multiple of 6 (60 = 6 × 10) and also a multiple of 15 (60 = 15 × 4).
  • There are infinitely many common multiples of 6 and 15.
  • If the number "v" is a multiple of the numbers "a" and "b", then all the multiples of "v" are also multiples of "a" and "b".
  • The common multiples of 6 and 15 are the numbers 30, 60, 90, 120, and so on.
  • Out of these, 30 is the smallest, 30 is the least common multiple (lcm) of 6 and 15.
  • Note: The prime factorization of a number: finding the prime numbers that multiply together to give that number.
  • If e = lcm (a, b), then the prime factorization of "e" must contain all the prime factors involved in the prime factorization of "a" and "b" taken by the highest power.
  • Example:
  • 40 = 23 × 5
  • 36 = 22 × 32
  • 126 = 2 × 32 × 7
  • lcm (40, 36, 126) = 23 × 32 × 5 × 7 = 2,520
  • Note: 23 = 2 × 2 × 2 = 8. We are saying that 2 was raised to the power of 3. Or, shorter, 2 to the power of 3. In this example 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 23 is the power and 8 is the value of the power:
  • Another example of calculating the least common multiple, lcm:
  • 938 = 2 × 7 × 67
  • 982 = 2 × 491
  • 743 = is a prime number and cannot be broken down into other prime factors
  • lcm (938, 982, 743) = 2 × 7 × 67 × 491 × 743 = 342,194,594
  • If two or more numbers have no common factors (they are coprime), then their least common multiple is calculated by simply multiplying the numbers.
  • Example:
  • 6 = 2 × 3
  • 35 = 5 × 7
  • lcm (6, 35) = 2 × 3 × 5 × 7 = 6 × 35 = 210