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Question

Using fundamental theorem of Arithmetic find L.C.M. and H.C.F of 816 and 170.
  1. L.C.M. =4080 and H.C.F =34
  2. L.C.M. =8160 and H.C.F =68
  3. L.C.M. =2048 and H.C.F =62
  4. L.C.M. =2040 and H.C.F =72

A
L.C.M. =4080 and H.C.F =34
B
L.C.M. =2048 and H.C.F =62
C
L.C.M. =8160 and H.C.F =68
D
L.C.M. =2040 and H.C.F =72
Solution
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According to the fundamental theorem of arithmetic every composite number can be factorised as a product of primes and this factorization is unique apart from the order in which the prime factor occurs.
  • Fundamental theorem of arithmetic is also called unique factorization theorem.
  • Composite number = product of prime numbers.
  • Any Integer greater than 1, either be a prime number or can be written as a product of prime factors.

The prime factors of 816=2×2×2×2×3×17=24×3×17

The prime factors of 170=2×5×17

LCM of 816 and 170=24×3×5×17=4080

HCF of 816 and 170=2×17=34
Option A.

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