LCM of 8,642 and 86,420, the Least (Lowest) Common Multiple Calculator. LCD, The Lowest Common Denominator. Find More Multiples Starting From LCM

Calculator of the LCM of 8,642 and 86,420, the least (lowest) common multiple of the numbers. The common denominator. More multiples


Used methods: 1. The divisibility of numbers. 2. The prime factorization of numbers

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
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lcm (8,642; 86,420) = ?

Method 1. The divisibility of numbers:

A number 'a' is divisible by a number 'b' if there is no remainder when 'a' is divided by 'b'.


Divide the larger number by the smaller one.

When we divide our numbers, there is no remainder:

86,420 ÷ 8,642 = 10 + 0

⇒ 86,420 = 8,642 × 10

⇒ 86,420 is divisible by 8,642.

⇒ 86,420 is a multiple of 8,642.

The smallest multiple of 86,420 is the number itself: 86,420.

» Online calculator. The divisibility of numbers


The least common multiple:
lcm (8,642; 86,420) = 86,420 = 22 × 5 × 29 × 149
86,420 is a multiple of 8,642
Scroll down for the 2nd method...

Method 2. The prime factorization:

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


8,642 = 2 × 29 × 149
8,642 is not a prime number but a composite one.

86,420 = 22 × 5 × 29 × 149
86,420 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 (8,642; 86,420) = 22 × 5 × 29 × 149 = 86,420
86,420 contains all the prime factors of the number 8,642

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 8,642 and 86,420:

    • 86,420 × 0 = 0

    • 86,420 × 2 = 172,840 

    • 86,420 × 3 = 259,260

    • ...

  • 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.


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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