find the l.c.m and h.c.f of 72 and 108, 306 and 657
Answers
Answer:
1. Expanding 72 as a product of prime numbers using prime factorisation method, we get
72=2×2×2×3×372=23×32…(1)
Expanding 108 as a product of prime numbers using prime factorisation method, we get
108=2×2×3×3×3108=22×33…(2)
From equation (1) and equation (2), we concluded that common factors are two 2’s and two 3’s while the extra factor is one 2 in 72 and one 3 in 108.
So, L.C.M of 72 and 108 can be expressed as:
=2×2×2×3×3×3=216
H.C.F of 72 and 108 can be expressed as:
=2×2×3×3=36
Thus, L.C.M and H.C.F of 72 and 108 are 216 and 36 respectively.
2. Given that 306 and 657
306 = 2 x 153,
=2 x 3 x 51,
=2 x 3 x 3 x 17
=21 x 32 x 171. 657
=3∗219 =3 x 3 x 73
=32∗731.
∴ HCF of 306 and 657=32=9.
∴ LCM of 306 and 657
=2 x 32 x 17 x 73=22338.
