Stage 7 · Factors & multiples
Lowest common multiple
Short division: divisors × last quotients.
How to do it
Method
Short division: divisors × last quotients
6, 8 → 3, 4: 2 × 3 × 4 = 24
Another way
Short division, or listing
Multiples of 6: 6, 12, 18, 24; of 8: 8, 16, 24 → 24
In full
Use short division: divide both numbers by a factor they share, and keep going until the two quotients share no factor but 1; the divisors and the last two quotients multiplied are the L.C.M. 6 and 8: ÷ 2 → 3 and 4; 3 and 4 share nothing but 1, and 2 × 3 = 6, 6 × 4 = 24, so the L.C.M. is 24. If the two numbers share no factor but 1 to begin with, the L.C.M. is the two multiplied: 3 and 5 → 3 × 5 = 15. Another way is listing: write out the multiples of both numbers and pick the smallest they share — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
L.C.M. of 5 and 4 = ?
Show the answer and working
Answer: L.C.M. of 5 and 4 = 20
L.C.M. of 5 and 4: 5 and 4 share no factor but 1, so the L.C.M. is the two multiplied: 5 × 4 = 20
Example 2
L.C.M. of 14 and 5 = ?
Show the answer and working
Answer: L.C.M. of 14 and 5 = 70
L.C.M. of 14 and 5: 14 and 5 share no factor but 1, so the L.C.M. is the two multiplied: 14 × 5 = 70
Example 3
L.C.M. of 15 and 8 = ?
Show the answer and working
Answer: L.C.M. of 15 and 8 = 120
L.C.M. of 15 and 8: 15 and 8 share no factor but 1, so the L.C.M. is the two multiplied: 15 × 8 = 120
Example 4
L.C.M. of 10 and 6 = ?
Show the answer and working
Answer: L.C.M. of 10 and 6 = 30
L.C.M. of 10 and 6: by short division, 10 and 6 ÷ 2 → 5 and 3; 5 and 3 share no factor but 1. Multiply the divisors and the last two numbers: 2 × 5 = 10, 10 × 3 = 30, so the L.C.M. is 30
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