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Find the HCF and LCM of the following integers by applying the prime factorization method 40, 36 and 126.
  • a)
    2, 2520
  • b)
    2, 2525
  • c)
    2, 2530
  • d)
    2, 2535
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the HCF and LCM of the following integers by applying the prime ...
40 = 2 x 2 x 2 x 5 = 23 x 5
36 = 2 x 2 x 3 x 3 = 22 x 32
and 126 = 2 x 3 x 3 x 7 = 2 x 32 x 7
For H.C.F taking minimum power of common factor H.C.F = (2)1 = 2
For L.C.M, taking maximum power of prime factors LC.M = 23 x 32 x 5 x 7 = 8 x 9 x 5 x 7 = 2520
Hence, H.C.F = 2 L.C.M = 2520
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Most Upvoted Answer
Find the HCF and LCM of the following integers by applying the prime ...
Prime Factorization of
40 = 2 × 2 × 2 × 5 = 23 × 5

Prime Factorization of 36 = 2 × 2 × 3 × 3 = 22 × 32

Prime Factorization of 126 = 2 × 3 × 3 × 7 = 2 × 32 × 7

LCM is the product of all prime factors, the greatest number of times they occur in either number.

LCM(40, 36, 126) = 23 × 32 × 5 × 7

= 8 × 9 × 5 × 7

= 2,520

So, LCM of 40, 36 and 126 = 2520
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Community Answer
Find the HCF and LCM of the following integers by applying the prime ...
To find the HCF and LCM of the given numbers (40, 36, and 126), we will follow the prime factorization method.

Prime factorization of 40:
40 can be expressed as 2 × 2 × 2 × 5.

Prime factorization of 36:
36 can be expressed as 2 × 2 × 3 × 3.

Prime factorization of 126:
126 can be expressed as 2 × 3 × 3 × 7.

HCF (Highest Common Factor):
The HCF is the product of the common prime factors of the given numbers.

Common prime factors of 40, 36, and 126:
The common prime factors are 2 and 3.

HCF = 2 × 3 = 6.

So, the HCF of 40, 36, and 126 is 6.

LCM (Least Common Multiple):
The LCM is the product of all the prime factors of the given numbers, considering each prime factor only once and with the highest power.

Prime factors of 40, 36, and 126:
The prime factors are 2, 2, 2, 3, 3, and 7.

LCM = 2 × 2 × 2 × 3 × 3 × 7 = 252.

So, the LCM of 40, 36, and 126 is 252.

Therefore, option 'A' (2, 2520) is the correct answer.
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Find the HCF and LCM of the following integers by applying the prime factorization method 40, 36 and 126.a)2, 2520b)2, 2525c)2, 2530d)2, 2535Correct answer is option 'A'. Can you explain this answer?
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