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 = 2^{3} × 5

36 = 2^{2} × 3^{2}

126 = 2 × 3^{2} × 7

lcm (40, 36, 126) = 2^{3} × 3^{2} × 5 × 7 = 2,520

Note: 2^{3} = 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. 2^{3} 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