JAMB 1986 · UME · Q3

Divide the L.C.M. of 48, 64 and 80 by their H.C.F.

Worked solution (try it first)
  1. Write each number as a product of primes: 48=24×348 = 2^4 \times 3, 64=2664 = 2^6 and 80=24×580 = 2^4 \times 5.
  2. The LCM takes the highest power of every prime: 26×3×5=9602^6 \times 3 \times 5 = 960.
  3. The HCF takes the lowest power of the primes common to all three: only 2 is common, so the HCF is 24=162^4 = 16.
  4. So 960÷16=60960 \div 16 = 60, option D.

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