What is the Least Common Multiple of 762 and 782?
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 762 and 782 is 297942.
LCM(762,782) = 297942
Least Common Multiple of 762 and 782 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 762 and 782, than apply into the LCM equation.
GCF(762,782) = 2
LCM(762,782) = ( 762 × 782) / 2
LCM(762,782) = 595884 / 2
LCM(762,782) = 297942
Least Common Multiple (LCM) of 762 and 782 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 762 and 782. First we will calculate the prime factors of 762 and 782.
Prime Factorization of 762
Prime factors of 762 are 2, 3, 127. Prime factorization of 762 in exponential form is:
762 = 21 × 31 × 1271
Prime Factorization of 782
Prime factors of 782 are 2, 17, 23. Prime factorization of 782 in exponential form is:
782 = 21 × 171 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 762 and 782.
LCM(762,782) = 21 × 31 × 1271 × 171 × 231
LCM(762,782) = 297942
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