What is the Least Common Multiple of 61680 and 61700?
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 61680 and 61700 is 190282800.
LCM(61680,61700) = 190282800
Least Common Multiple of 61680 and 61700 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61680 and 61700, than apply into the LCM equation.
GCF(61680,61700) = 20
LCM(61680,61700) = ( 61680 × 61700) / 20
LCM(61680,61700) = 3805656000 / 20
LCM(61680,61700) = 190282800
Least Common Multiple (LCM) of 61680 and 61700 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 61680 and 61700. First we will calculate the prime factors of 61680 and 61700.
Prime Factorization of 61680
Prime factors of 61680 are 2, 3, 5, 257. Prime factorization of 61680 in exponential form is:
61680 = 24 × 31 × 51 × 2571
Prime Factorization of 61700
Prime factors of 61700 are 2, 5, 617. Prime factorization of 61700 in exponential form is:
61700 = 22 × 52 × 6171
Now multiplying the highest exponent prime factors to calculate the LCM of 61680 and 61700.
LCM(61680,61700) = 24 × 31 × 52 × 2571 × 6171
LCM(61680,61700) = 190282800
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