Worked Example 1
Find the HCF and LCM of 60 and 72.
Step 1: prime factors of each60 = 2×2×3×5 and 72 = 2×2×2×3×3
Step 2: HCFHCF = 2 × 2 × 3 = 12
Step 3: LCMLCM = 2×2×2 × 3×3 × 5 = 360
Check with the product rule12 × 360 = 4320 = 60 × 72. And 12 < 60 while 360 > 72, as they must be.
Worked Example 2
A floor is 240 cm by 180 cm. What is the largest square tile that fits exactly, with no cutting?
Decide which you needThe tile must divide into both, and you want the largest such number: the HCF.
FactoriseCommon primes at the lowest power: 2 × 2 × 3 × 5
AnswerThe largest tile is 60 cm by 60 cm.
How many tiles?4 along one side and 3 along the other, so 12 tiles.
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