What is the Least Common Multiple of 748 and 752?
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 748 and 752 is 140624.
LCM(748,752) = 140624
Least Common Multiple of 748 and 752 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 748 and 752, than apply into the LCM equation.
GCF(748,752) = 4
LCM(748,752) = ( 748 × 752) / 4
LCM(748,752) = 562496 / 4
LCM(748,752) = 140624
Least Common Multiple (LCM) of 748 and 752 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 748 and 752. First we will calculate the prime factors of 748 and 752.
Prime Factorization of 748
Prime factors of 748 are 2, 11, 17. Prime factorization of 748 in exponential form is:
748 = 22 × 111 × 171
Prime Factorization of 752
Prime factors of 752 are 2, 47. Prime factorization of 752 in exponential form is:
752 = 24 × 471
Now multiplying the highest exponent prime factors to calculate the LCM of 748 and 752.
LCM(748,752) = 24 × 111 × 171 × 471
LCM(748,752) = 140624
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