What is the Least Common Multiple of 31716 and 31728?
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 31716 and 31728 is 83857104.
LCM(31716,31728) = 83857104
Least Common Multiple of 31716 and 31728 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31716 and 31728, than apply into the LCM equation.
GCF(31716,31728) = 12
LCM(31716,31728) = ( 31716 × 31728) / 12
LCM(31716,31728) = 1006285248 / 12
LCM(31716,31728) = 83857104
Least Common Multiple (LCM) of 31716 and 31728 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31716 and 31728. First we will calculate the prime factors of 31716 and 31728.
Prime Factorization of 31716
Prime factors of 31716 are 2, 3, 881. Prime factorization of 31716 in exponential form is:
31716 = 22 × 32 × 8811
Prime Factorization of 31728
Prime factors of 31728 are 2, 3, 661. Prime factorization of 31728 in exponential form is:
31728 = 24 × 31 × 6611
Now multiplying the highest exponent prime factors to calculate the LCM of 31716 and 31728.
LCM(31716,31728) = 24 × 32 × 8811 × 6611
LCM(31716,31728) = 83857104
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