SSC & BANK EXAMS: QUANTITATIVE APTITUDE · NUMBER SYSTEM

HCF and LCM word problems

“Together again / least number” → LCM. “Greatest length / largest size that fits exactly” → HCF.

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Worked examples

Example 1 · level 1

Three temple bells in Varanasi ring at intervals of 4, 9, 18 seconds. If they ring together now, after how many seconds will they next ring together?

Show solution
  1. LCM(4, 9) = 36.
  2. LCM with 18 = 36.
  3. They ring together after 36 seconds.

Answer: 36 seconds

Example 2 · level 2

Three pieces of cloth at a shop in Surat measure 28 cm, 42 cm, 126 cm. What is the greatest length (in cm) of a measuring stick that can measure all three exactly?

Show solution
  1. HCF(28, 42) = 14.
  2. HCF with 126 = 14.

Answer: 14 cm

Example 3 · level 3

Find the greatest number that divides 41, 79, 134 leaving remainders 1, 9, 4 respectively.

Show solution
  1. Exact multiples: 40, 70, 130.
  2. HCF = 10.

Answer: 10

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