What is the Least Common Multiple of 345 and 352?
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 345 and 352 is 121440.
LCM(345,352) = 121440
Least Common Multiple of 345 and 352 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 352, than apply into the LCM equation.
GCF(345,352) = 1
LCM(345,352) = ( 345 × 352) / 1
LCM(345,352) = 121440 / 1
LCM(345,352) = 121440
Least Common Multiple (LCM) of 345 and 352 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 352. First we will calculate the prime factors of 345 and 352.
Prime Factorization of 345
Prime factors of 345 are 3, 5, 23. Prime factorization of 345 in exponential form is:
345 = 31 × 51 × 231
Prime Factorization of 352
Prime factors of 352 are 2, 11. Prime factorization of 352 in exponential form is:
352 = 25 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 352.
LCM(345,352) = 31 × 51 × 231 × 25 × 111
LCM(345,352) = 121440
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