Divide two numbers by common factors in one ladder and read off both the HCF and the LCM, then speed it up with bigger divisors.
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Divide both numbers by a common prime until they share nothing.
It's like the division method, with two numbers side by side. Divide both by a common prime and write both answers in the next row. Repeat until the two numbers have no common prime factor.
The book's ladders for 300 and 150, and for 630 and 770.
Problem. Find the HCF and the LCM of 300 and 150, and of 630 and 770, with ladders. (Textbook p. 61)
Dividing by a bigger common factor saves steps.
"For 300 and 150, I can first divide both by 50."
HCF and LCM .
HCF = side divisors; LCM = side divisors × bottom row.
Fill in a fast ladder with a big common factor.
Try This, Textbook p. 62 (a): use a fast ladder for 90 and 150.
Divide both by 30: 90 ÷ 30 = and 150 ÷ 30 = .
3 and 5 share no factor, so stop.
HCF = . LCM = 30 × 3 × 5 = .
Use the ladder to find the HCF and LCM of two pairs.
Use the ladder method. Divide by any common factor you can spot.
Write each divisor and row.
Divisors, then divisors × bottom row.
Write each divisor and row.
Same rule.