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What is the Least Common Multiple of 1972 and 1990?

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 1972 and 1990 is 1962140.

LCM(1972,1990) = 1962140

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Least Common Multiple of 1972 and 1990 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1972 and 1990, than apply into the LCM equation.

GCF(1972,1990) = 2
LCM(1972,1990) = ( 1972 × 1990) / 2
LCM(1972,1990) = 3924280 / 2
LCM(1972,1990) = 1962140

Least Common Multiple (LCM) of 1972 and 1990 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1972 and 1990. First we will calculate the prime factors of 1972 and 1990.

Prime Factorization of 1972

Prime factors of 1972 are 2, 17, 29. Prime factorization of 1972 in exponential form is:

1972 = 22 × 171 × 291

Prime Factorization of 1990

Prime factors of 1990 are 2, 5, 199. Prime factorization of 1990 in exponential form is:

1990 = 21 × 51 × 1991

Now multiplying the highest exponent prime factors to calculate the LCM of 1972 and 1990.

LCM(1972,1990) = 22 × 171 × 291 × 51 × 1991
LCM(1972,1990) = 1962140