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Real Numbers

Question

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Find the LCM and HCF of 1296 and 2520 by the prime factorisation method.

Solution

Since,

1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

= 2⁴ × 3⁴

and 2520 = 2 × 2 × 2 × 3 × 3 × 5 × 7

= 2³ × 3² × 5 × 7

∴ LCM = Product of each prime factor with highest powers

= 2⁴ × 3⁴ × 5 × 7 = 45360

i.e., LCM (1296, 2520)= 45360

H.C.F. = Product of common prime factors with lowest powers

= 2³ × 3² = 8 × 9 = 72

i.e., H.C.F. (1296, 2520) = 72.

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