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What is the Least Common Multiple of 1971 and 1988?

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 1988 is 3918348.

LCM(1971,1988) = 3918348

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Least Common Multiple of 1971 and 1988 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 1988, than apply into the LCM equation.

GCF(1971,1988) = 1
LCM(1971,1988) = ( 1971 × 1988) / 1
LCM(1971,1988) = 3918348 / 1
LCM(1971,1988) = 3918348

Least Common Multiple (LCM) of 1971 and 1988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1971 and 1988. First we will calculate the prime factors of 1971 and 1988.

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 1988

Prime factors of 1988 are 2, 7, 71. Prime factorization of 1988 in exponential form is:

1988 = 22 × 71 × 711

Now multiplying the highest exponent prime factors to calculate the LCM of 1971 and 1988.

LCM(1971,1988) = 33 × 731 × 22 × 71 × 711
LCM(1971,1988) = 3918348