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What is the Least Common Multiple of 1921 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 1921 and 1938 is 218994.

LCM(1921,1938) = 218994

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Least Common Multiple of 1921 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 1921 and 1938, than apply into the LCM equation.

GCF(1921,1938) = 17
LCM(1921,1938) = ( 1921 × 1938) / 17
LCM(1921,1938) = 3722898 / 17
LCM(1921,1938) = 218994

Least Common Multiple (LCM) of 1921 and 1938 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1921 and 1938. First we will calculate the prime factors of 1921 and 1938.

Prime Factorization of 1921

Prime factors of 1921 are 17, 113. Prime factorization of 1921 in exponential form is:

1921 = 171 × 1131

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 1921 and 1938.

LCM(1921,1938) = 171 × 1131 × 21 × 31 × 191
LCM(1921,1938) = 218994