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Least Common Multiple of 78 and 690

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 690 is 8970.

LCM(78,690) = 8970

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Least Common Multiple of 78 and 690 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 690, than apply into the LCM equation.

GCF(78,690) = 6
LCM(78,690) = ( 78 × 690) / 6
LCM(78,690) = 53820 / 6
LCM(78,690) = 8970

Least Common Multiple (LCM) of 78 and 690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 690. First we will calculate the prime factors of 78 and 690.

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 690

Prime factors of 690 are 2, 3, 5, 23. Prime factorization of 690 in exponential form is:

690 = 21 × 31 × 51 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 690.

LCM(78,690) = 21 × 31 × 131 × 51 × 231
LCM(78,690) = 8970

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