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What is the Least Common Multiple of 1918 and 1938?

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 1918 and 1938 is 1858542.

LCM(1918,1938) = 1858542

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Least Common Multiple of 1918 and 1938 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1918 and 1938, than apply into the LCM equation.

GCF(1918,1938) = 2
LCM(1918,1938) = ( 1918 × 1938) / 2
LCM(1918,1938) = 3717084 / 2
LCM(1918,1938) = 1858542

Least Common Multiple (LCM) of 1918 and 1938 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1918 and 1938. First we will calculate the prime factors of 1918 and 1938.

Prime Factorization of 1918

Prime factors of 1918 are 2, 7, 137. Prime factorization of 1918 in exponential form is:

1918 = 21 × 71 × 1371

Prime Factorization of 1938

Prime factors of 1938 are 2, 3, 17, 19. Prime factorization of 1938 in exponential form is:

1938 = 21 × 31 × 171 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 1918 and 1938.

LCM(1918,1938) = 21 × 71 × 1371 × 31 × 171 × 191
LCM(1918,1938) = 1858542