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What is the Least Common Multiple of 7458 and 7470?

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 7458 and 7470 is 9285210.

LCM(7458,7470) = 9285210

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Least Common Multiple of 7458 and 7470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7458 and 7470, than apply into the LCM equation.

GCF(7458,7470) = 6
LCM(7458,7470) = ( 7458 × 7470) / 6
LCM(7458,7470) = 55711260 / 6
LCM(7458,7470) = 9285210

Least Common Multiple (LCM) of 7458 and 7470 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7458 and 7470. First we will calculate the prime factors of 7458 and 7470.

Prime Factorization of 7458

Prime factors of 7458 are 2, 3, 11, 113. Prime factorization of 7458 in exponential form is:

7458 = 21 × 31 × 111 × 1131

Prime Factorization of 7470

Prime factors of 7470 are 2, 3, 5, 83. Prime factorization of 7470 in exponential form is:

7470 = 21 × 32 × 51 × 831

Now multiplying the highest exponent prime factors to calculate the LCM of 7458 and 7470.

LCM(7458,7470) = 21 × 32 × 111 × 1131 × 51 × 831
LCM(7458,7470) = 9285210