Factors and multiples · Usually met around P4
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 except 1. Multiply the divisors and the last two quotients to get the L.C.M. 6 and 8: ÷ 2 → 3 and 4. 3 and 4 share no factor except 1, and 2 × 3 = 6, 6 × 4 = 24, so the L.C.M. is 24. If the two numbers share no factor except 1 to start with, the L.C.M. is the two numbers multiplied: 3 and 5 → 3 × 5 = 15. Another way is listing: write out the multiples of both numbers and pick the smallest one they share.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
L.C.M. of 6 and 7 = ?
Show the answer and working
Answer: L.C.M. of 6 and 7 = 42
L.C.M. of 6 and 7: 6 and 7 share no factor but 1, so the L.C.M. is the two multiplied: 6 × 7 = 42
Example 2
L.C.M. of 4 and 11 = ?
Show the answer and working
Answer: L.C.M. of 4 and 11 = 44
L.C.M. of 4 and 11: 4 and 11 share no factor but 1, so the L.C.M. is the two multiplied: 4 × 11 = 44
Example 3
L.C.M. of 15 and 2 = ?
Show the answer and working
Answer: L.C.M. of 15 and 2 = 30
L.C.M. of 15 and 2: 15 and 2 share no factor but 1, so the L.C.M. is the two multiplied: 15 × 2 = 30
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