Question

Find the HCF of 86 and 404 by prime factorization method. Hence find their LCM.

Answer 1

Answer:

Answer............ ➹

Answer 2

Step-by-step explanation:

96=2×2×2×2×2×3

404=2×2×101

96=2×2×2×2×2×3

404=2×2×101

Here we can see that the 2×2=42×2=4 is the highest common factor of 96 and 404.

To find the LCM (Lowest Common Multiple) we need not calculate it from the beginning but by a simple rule given below:

If a and b are two numbers then

a×b=(H.C.F of a and b)×(L.C.M of a and b)

a×b=(H.C.F of a and b)×(L.C.M of a and b)

Therefore, after rearrangement we can write

Therefore, L.C.M of 96 and 404 is given by

L.C.M of 96 and 404 = 96×404H.C.F of 96 and 404=96×4044=96×101=9696L.C.M of 96 and 404 = 96×404H.C.F of 96 and 404=96×4044=96×101=9696

Hence, L.C.M of 96 and 404 is 9696.

Note: We can verify the result obtained by evaluating the L.C.M 96 and 404 by prime factorization method

96=2×2×2×2×2×3404=2×2×10196=2×2×2×2×2×3404=2×2×101

Thus, L.C.M of 96 and 404 is 2×2×2×2×2×3×101=32×3×101=96×101=96962×2×2×2×2×3×101=32×3×101=96×101=9696