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What is the Least Common Multiple of 76990 and 77000?

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 76990 and 77000 is 592823000.

LCM(76990,77000) = 592823000

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Least Common Multiple of 76990 and 77000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76990 and 77000, than apply into the LCM equation.

GCF(76990,77000) = 10
LCM(76990,77000) = ( 76990 × 77000) / 10
LCM(76990,77000) = 5928230000 / 10
LCM(76990,77000) = 592823000

Least Common Multiple (LCM) of 76990 and 77000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76990 and 77000. First we will calculate the prime factors of 76990 and 77000.

Prime Factorization of 76990

Prime factors of 76990 are 2, 5, 7699. Prime factorization of 76990 in exponential form is:

76990 = 21 × 51 × 76991

Prime Factorization of 77000

Prime factors of 77000 are 2, 5, 7, 11. Prime factorization of 77000 in exponential form is:

77000 = 23 × 53 × 71 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 76990 and 77000.

LCM(76990,77000) = 23 × 53 × 76991 × 71 × 111
LCM(76990,77000) = 592823000