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What is the Least Common Multiple of 1967 and 1980?

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 1967 and 1980 is 3894660.

LCM(1967,1980) = 3894660

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Least Common Multiple of 1967 and 1980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1967 and 1980, than apply into the LCM equation.

GCF(1967,1980) = 1
LCM(1967,1980) = ( 1967 × 1980) / 1
LCM(1967,1980) = 3894660 / 1
LCM(1967,1980) = 3894660

Least Common Multiple (LCM) of 1967 and 1980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1967 and 1980. First we will calculate the prime factors of 1967 and 1980.

Prime Factorization of 1967

Prime factors of 1967 are 7, 281. Prime factorization of 1967 in exponential form is:

1967 = 71 × 2811

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

Now multiplying the highest exponent prime factors to calculate the LCM of 1967 and 1980.

LCM(1967,1980) = 71 × 2811 × 22 × 32 × 51 × 111
LCM(1967,1980) = 3894660