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What is the Least Common Multiple of 7650 and 7658?

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 7650 and 7658 is 29291850.

LCM(7650,7658) = 29291850

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Least Common Multiple of 7650 and 7658 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7650 and 7658, than apply into the LCM equation.

GCF(7650,7658) = 2
LCM(7650,7658) = ( 7650 × 7658) / 2
LCM(7650,7658) = 58583700 / 2
LCM(7650,7658) = 29291850

Least Common Multiple (LCM) of 7650 and 7658 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7650 and 7658. First we will calculate the prime factors of 7650 and 7658.

Prime Factorization of 7650

Prime factors of 7650 are 2, 3, 5, 17. Prime factorization of 7650 in exponential form is:

7650 = 21 × 32 × 52 × 171

Prime Factorization of 7658

Prime factors of 7658 are 2, 7, 547. Prime factorization of 7658 in exponential form is:

7658 = 21 × 71 × 5471

Now multiplying the highest exponent prime factors to calculate the LCM of 7650 and 7658.

LCM(7650,7658) = 21 × 32 × 52 × 171 × 71 × 5471
LCM(7650,7658) = 29291850