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What is the Least Common Multiple of 1971 and 1978?

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 1971 and 1978 is 3898638.

LCM(1971,1978) = 3898638

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Least Common Multiple of 1971 and 1978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1971 and 1978, than apply into the LCM equation.

GCF(1971,1978) = 1
LCM(1971,1978) = ( 1971 × 1978) / 1
LCM(1971,1978) = 3898638 / 1
LCM(1971,1978) = 3898638

Least Common Multiple (LCM) of 1971 and 1978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1971 and 1978. First we will calculate the prime factors of 1971 and 1978.

Prime Factorization of 1971

Prime factors of 1971 are 3, 73. Prime factorization of 1971 in exponential form is:

1971 = 33 × 731

Prime Factorization of 1978

Prime factors of 1978 are 2, 23, 43. Prime factorization of 1978 in exponential form is:

1978 = 21 × 231 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 1971 and 1978.

LCM(1971,1978) = 33 × 731 × 21 × 231 × 431
LCM(1971,1978) = 3898638