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What is the Least Common Multiple of 68992 and 69003?

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 68992 and 69003 is 432786816.

LCM(68992,69003) = 432786816

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Least Common Multiple of 68992 and 69003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68992 and 69003, than apply into the LCM equation.

GCF(68992,69003) = 11
LCM(68992,69003) = ( 68992 × 69003) / 11
LCM(68992,69003) = 4760654976 / 11
LCM(68992,69003) = 432786816

Least Common Multiple (LCM) of 68992 and 69003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 68992 and 69003. First we will calculate the prime factors of 68992 and 69003.

Prime Factorization of 68992

Prime factors of 68992 are 2, 7, 11. Prime factorization of 68992 in exponential form is:

68992 = 27 × 72 × 111

Prime Factorization of 69003

Prime factors of 69003 are 3, 11, 17, 41. Prime factorization of 69003 in exponential form is:

69003 = 32 × 111 × 171 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 68992 and 69003.

LCM(68992,69003) = 27 × 72 × 111 × 32 × 171 × 411
LCM(68992,69003) = 432786816