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What is the Least Common Multiple of 68 and 72?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 68 and 72 is 1224.

LCM(68,72) = 1224

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Least Common Multiple of 68 and 72 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68 and 72, than apply into the LCM equation.

GCF(68,72) = 4
LCM(68,72) = ( 68 × 72) / 4
LCM(68,72) = 4896 / 4
LCM(68,72) = 1224

Least Common Multiple (LCM) of 68 and 72 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 68 and 72. First we will calculate the prime factors of 68 and 72.

Prime Factorization of 68

Prime factors of 68 are 2, 17. Prime factorization of 68 in exponential form is:

68 = 22 × 171

Prime Factorization of 72

Prime factors of 72 are 2, 3. Prime factorization of 72 in exponential form is:

72 = 23 × 32

Now multiplying the highest exponent prime factors to calculate the LCM of 68 and 72.

LCM(68,72) = 23 × 171 × 32
LCM(68,72) = 1224

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