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