Question

Find the lcm and hcf of 18,24,60,150

Answer 1

L.C.M( least common multiple ) of 18,24,60 150 is 1800

H.C.F ( highest common multiple) of 18,24,60,150 is 6
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Answer 2

Answer:

$\fbox{\underline{\Huge{\texttt{LCM = 1800, HCF = 6}}}}$

Step-by-step explanation:

LCM (18, 24, 60, 150):

Prime factorization of 18 = 2 × 3 × 3  = $2^1\times3^2$

Prime factorization of 24 = 2 × 2 × 2 × 3 = $2^3\times3^1$

Prime factorization of 60 = 2 × 2 × 3 × 5  = $2^2\times3^1\times5^1$

Prime factorization of 150 = 2 × 3 × 5 × 5 = $2^1\times3^1\times5^2$

Using the set of prime numbers from each set with the highest exponent value we take $2^3\times3^2\times5^2$ = 1800

Therefore LCM(18, 24, 60, 150) = 1800

HCF (18, 24, 60, 150):

The prime factorization of 18 is 2 × 3 × 3  = 18

The prime factorization of 24 is 2 × 2 × 2 × 3 = 24

The prime factorization of 60 is 2 × 2 × 3 × 5 = 60

The prime factorization of 150 is 2 × 3 × 5 × 5 = 150

The occurrences of common prime factors of 18, 24, 60 and 150 is 2 and 3.

So the HCF of 18, 24, 60 and 150 is 2 × 3 = 6