Question

1. Find the LCM of the following numbers by the prime factorization method :

(b) 27 , 45​

Answer 1

Answer:

Least Common Multiple of 27 and 45 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 27 and 45, than apply into the LCM equation.

GCF(27,45) = 9

LCM(27,45) = ( 27 × 45) / 9

LCM(27,45) = 1215 / 9

LCM(27,45) = 135

Least Common Multiple (LCM) of 27 and 45 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27 and 45. First we will calculate the prime factors of 27 and 45.

Prime Factorization of 27

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 33

Prime Factorization of 45

Prime factors of 45 are 3, 5. Prime factorization of 45 in exponential form is:

45 = 32 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 27 and 45.

LCM(27,45) = 33 × 51

LCM(27,45) = 135

Answer 2

Step-by-step explanation:

27=3×3×3

=3 cube

45=5×3×3

LCM of 27 and 45 is 27×5=135