What is the Least Common Multiple of 10728 and 10742?
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 10728 and 10742 is 57620088.
LCM(10728,10742) = 57620088
Least Common Multiple of 10728 and 10742 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10728 and 10742, than apply into the LCM equation.
GCF(10728,10742) = 2
LCM(10728,10742) = ( 10728 × 10742) / 2
LCM(10728,10742) = 115240176 / 2
LCM(10728,10742) = 57620088
Least Common Multiple (LCM) of 10728 and 10742 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 10728 and 10742. First we will calculate the prime factors of 10728 and 10742.
Prime Factorization of 10728
Prime factors of 10728 are 2, 3, 149. Prime factorization of 10728 in exponential form is:
10728 = 23 × 32 × 1491
Prime Factorization of 10742
Prime factors of 10742 are 2, 41, 131. Prime factorization of 10742 in exponential form is:
10742 = 21 × 411 × 1311
Now multiplying the highest exponent prime factors to calculate the LCM of 10728 and 10742.
LCM(10728,10742) = 23 × 32 × 1491 × 411 × 1311
LCM(10728,10742) = 57620088
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