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What is the Least Common Multiple of 1980 and 1999?

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 1980 and 1999 is 3958020.

LCM(1980,1999) = 3958020

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Least Common Multiple of 1980 and 1999 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1980 and 1999, than apply into the LCM equation.

GCF(1980,1999) = 1
LCM(1980,1999) = ( 1980 × 1999) / 1
LCM(1980,1999) = 3958020 / 1
LCM(1980,1999) = 3958020

Least Common Multiple (LCM) of 1980 and 1999 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1980 and 1999. First we will calculate the prime factors of 1980 and 1999.

Prime Factorization of 1980

Prime factors of 1980 are 2, 3, 5, 11. Prime factorization of 1980 in exponential form is:

1980 = 22 × 32 × 51 × 111

Prime Factorization of 1999

Prime factors of 1999 are 1999. Prime factorization of 1999 in exponential form is:

1999 = 19991

Now multiplying the highest exponent prime factors to calculate the LCM of 1980 and 1999.

LCM(1980,1999) = 22 × 32 × 51 × 111 × 19991
LCM(1980,1999) = 3958020