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What is the Least Common Multiple of 67920 and 67940?

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 67920 and 67940 is 230724240.

LCM(67920,67940) = 230724240

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Least Common Multiple of 67920 and 67940 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67920 and 67940, than apply into the LCM equation.

GCF(67920,67940) = 20
LCM(67920,67940) = ( 67920 × 67940) / 20
LCM(67920,67940) = 4614484800 / 20
LCM(67920,67940) = 230724240

Least Common Multiple (LCM) of 67920 and 67940 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67920 and 67940. First we will calculate the prime factors of 67920 and 67940.

Prime Factorization of 67920

Prime factors of 67920 are 2, 3, 5, 283. Prime factorization of 67920 in exponential form is:

67920 = 24 × 31 × 51 × 2831

Prime Factorization of 67940

Prime factors of 67940 are 2, 5, 43, 79. Prime factorization of 67940 in exponential form is:

67940 = 22 × 51 × 431 × 791

Now multiplying the highest exponent prime factors to calculate the LCM of 67920 and 67940.

LCM(67920,67940) = 24 × 31 × 51 × 2831 × 431 × 791
LCM(67920,67940) = 230724240