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What is the Least Common Multiple of 63 and 78?

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 63 and 78 is 1638.

LCM(63,78) = 1638

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Least Common Multiple of 63 and 78 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 63 and 78, than apply into the LCM equation.

GCF(63,78) = 3
LCM(63,78) = ( 63 × 78) / 3
LCM(63,78) = 4914 / 3
LCM(63,78) = 1638

Least Common Multiple (LCM) of 63 and 78 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 63 and 78. First we will calculate the prime factors of 63 and 78.

Prime Factorization of 63

Prime factors of 63 are 3, 7. Prime factorization of 63 in exponential form is:

63 = 32 × 71

Prime Factorization of 78

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

78 = 21 × 31 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 63 and 78.

LCM(63,78) = 32 × 71 × 21 × 131
LCM(63,78) = 1638

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