# Calculate the least common multiple, LCM, by two methods: either the prime factorization of numbers, numbers' divisibility, or the Euclidean algorithm

## The least common multiple, LCM: the latest 13 calculated values

 The LCM of 2,316 and 1,176 = ? Sep 29 08:42 UTC (GMT) The LCM of 237,664 and 1,663,697 = ? Sep 29 08:42 UTC (GMT) The LCM of 26 and 52 = ? Sep 29 08:42 UTC (GMT) The LCM of 7,689 and 4,738 = ? Sep 29 08:42 UTC (GMT) The LCM of 36 and 37 = ? Sep 29 08:42 UTC (GMT) The LCM of 144 and 121 = ? Sep 29 08:42 UTC (GMT) The LCM of 27,513,918 and 165,083,508 = ? Sep 29 08:42 UTC (GMT) The LCM of 60 and 144 = ? Sep 29 08:42 UTC (GMT) The LCM of 48 and 500 = ? Sep 29 08:42 UTC (GMT) The LCM of 9 and 15 = ? Sep 29 08:42 UTC (GMT) The LCM of 9 and 15 = ? Sep 29 08:42 UTC (GMT) The LCM of 70 and 136 = ? Sep 29 08:42 UTC (GMT) The LCM of 113 and 4,162 = ? Sep 29 08:42 UTC (GMT) The least common multiple, LCM: the list of all the operations

## 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:
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• 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