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What is the Least Common Multiple of 61740 and 61745?

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 61740 and 61745 is 762427260.

LCM(61740,61745) = 762427260

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Least Common Multiple of 61740 and 61745 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61740 and 61745, than apply into the LCM equation.

GCF(61740,61745) = 5
LCM(61740,61745) = ( 61740 × 61745) / 5
LCM(61740,61745) = 3812136300 / 5
LCM(61740,61745) = 762427260

Least Common Multiple (LCM) of 61740 and 61745 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 61740 and 61745. First we will calculate the prime factors of 61740 and 61745.

Prime Factorization of 61740

Prime factors of 61740 are 2, 3, 5, 7. Prime factorization of 61740 in exponential form is:

61740 = 22 × 32 × 51 × 73

Prime Factorization of 61745

Prime factors of 61745 are 5, 53, 233. Prime factorization of 61745 in exponential form is:

61745 = 51 × 531 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 61740 and 61745.

LCM(61740,61745) = 22 × 32 × 51 × 73 × 531 × 2331
LCM(61740,61745) = 762427260