HCF & LCM · Topic 5 of 6

📏 Measurement & Timing

4 exam question types, fully solved

These are the “real life” word problems — tapes, cans, tiles, bells and runners. Every one is secretly an HCF or an LCM. The whole skill is deciding which.

HCF for “biggest that fits”, LCM for “when they meet”

• Use the HCF when you want the greatest size that goes into several quantities exactly: longest tape, biggest can/bucket, largest square tile, greatest weight.

Number of pieces / cans , summed. Number of square tiles (divide the area by HCF squared).

• Use the LCM when repeating events that start together next coincide: bells ringing, lights changing, runners returning to the start, or the least length several tapes can all measure.

Times they coincide in a window ; add 1 if the start is counted, not if it is excluded.

• Always convert to one unit first (m → cm, hr → min) before taking the HCF or LCM.

⚖️HCF & LCM MachineSame prime factors — lowest powers make the HCF, highest powers make the LCM

Bell A (s)

Bell B (s)

Bell C (optional)

● Bell A: every 6 s● Bell B: every 8 s● Bell C: every 12 s

Each dot is one toll: a bell with period p tolls at p, 2p, 3p… The tall green lines are where every row lines up — the common multiples, i.e. multiples of the LCM.

All together every LCM = 24 s

In 30 minutes = 1800 s: 1800 ÷ 24 = 75 times together — add 1 if you also count the start: 76.

The longest tape measuring both 12 m and 18 m exactly is m.

Q1The greatest tape that measures 12 m and 18 m exactly is:

Q2Bells ring every 4, 6 and 8 minutes. They next ring together after:

Q3The largest square tile for a 6 m × 4 m floor has side:

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Real exam questions — Measurement & Timing

4 question types · 15 solved examples from real SSC papers

Biggest tape, can or tile that fits exactly ⇒ HCF. First moment repeating events coincide ⇒ LCM. Convert to one unit before you start.

How to solve this type

When you need the GREATEST length, weight or measure that fits into several quantities a whole number of times, that is the HCF. Always convert everything to the SAME unit first (m to cm, etc.). If the question asks for the number of pieces, divide each length by the HCF and add the quotients.

The sides of a triangular field are 62 m, 186 m and 279 m. Find the greatest length of tape that can measure each side exactly.

A31 mB93 mC62 mD30 m

What is the greatest length (in cm) of tape that can measure 640 cm, 720 cm and 960 cm exactly?

A60B80C120D40

Rods of 24 m, 36 m and 48 m are cut into equal pieces without wastage. Find the minimum total number of pieces.

A11B12C10D9

What is the greatest length of tape that can exactly measure 10 m 54 cm and 11 m 56 cm?

A28 cmB42 cmC56 cmD34 cm