Find LCM & HCF


Q) LCM of 24, 42 and 28


Prime factorizations:



  • 24=23×3

  • 42=2×3×7

  • 28=22×7


Take highest powers: 23,  31,  71.


LCM = 23×3×7 = 8×3×7 = 168


Ans: 168


Q) HCF (GCD) of 42, 56 and 63


Prime factorizations:



  • 42=2×3×7

  • 56=23×7

  • 63=32×7


Common prime factors with lowest powers: only 71.


HCF = 7.


Ans: 7


3) LCM of 16a2bc3,  32abc,  64a3bc2


LCM of 16, 32, 64 = 64


Variables (take the highest powers)



  • For a: powers are 2, 1, 3 → highest = 3

  • For b: powers are 1, 1, 1 → highest = 1

  • For c: powers are 3, 1, 2 → highest = 3


Combine


So


LCM = 64a3b1c3


Ans: 64a3b1c3