How to find out if in a question the HCF or the LCM has to be found out?

Illustrative Examples

Example

Find the L.C.M. of 72, 240, 196.

Solution

Using Prime factorisation method
72 = 2×2×2×3×3 = 2³×3²
240 = 2×2×2×2×3×5 = 24×3×5
196 = 2×2×7×7 = 2²×7²
L.C.M. of the given numbers = product of all the prime factors of each of the given number with greatest index of common prime factors
= 24×3²×5×7² = 16×9×5×49 = 35280.

Example

Find the H.C.F. of 72, 126 and 270.

Solution

Using Prime factorisation method
72 = 2×2×2×3×3 = 2³×3²
126 = 2×3×3×7 = 21×3²×71
270 = 2×3×3×3×5 = 21×3³×51
H.C.F. of the given numbers = the product of common factors with least index
= 21×3² = 2×3×3 = 18

regards,

Team,

TopperLearning.

Answered by  | 24th Mar, 2010, 08:26: AM

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