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What is the Least Common Multiple of 78 and 92?

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 78 and 92 is 3588.

LCM(78,92) = 3588

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Least Common Multiple of 78 and 92 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78 and 92, than apply into the LCM equation.

GCF(78,92) = 2
LCM(78,92) = ( 78 × 92) / 2
LCM(78,92) = 7176 / 2
LCM(78,92) = 3588

Least Common Multiple (LCM) of 78 and 92 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 92. First we will calculate the prime factors of 78 and 92.

Prime Factorization of 78

Prime factors of 78 are 2, 3, 13. Prime factorization of 78 in exponential form is:

78 = 21 × 31 × 131

Prime Factorization of 92

Prime factors of 92 are 2, 23. Prime factorization of 92 in exponential form is:

92 = 22 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 92.

LCM(78,92) = 22 × 31 × 131 × 231
LCM(78,92) = 3588

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