What is the Least Common Multiple of 748 and 754?
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 754 is 281996.
LCM(748,754) = 281996
Least Common Multiple of 748 and 754 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 754, than apply into the LCM equation.
GCF(748,754) = 2
LCM(748,754) = ( 748 × 754) / 2
LCM(748,754) = 563992 / 2
LCM(748,754) = 281996
Least Common Multiple (LCM) of 748 and 754 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 748 and 754. First we will calculate the prime factors of 748 and 754.
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 754
Prime factors of 754 are 2, 13, 29. Prime factorization of 754 in exponential form is:
754 = 21 × 131 × 291
Now multiplying the highest exponent prime factors to calculate the LCM of 748 and 754.
LCM(748,754) = 22 × 111 × 171 × 131 × 291
LCM(748,754) = 281996
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