Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can find the greatest common factor and the least common multiple of two numbers, and use each to solve a real problem.
Key words
Find Factors and Multiples — Listing what divides a number evenly (its factors) and what it divides into evenly (its multiples), then finding what two numbers share.
Factor — A whole number that divides another number evenly, with no remainder.
Multiple — The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it.
Greatest common factor (GCF) — The largest number that is a factor of two or more numbers. It answers “how many equal groups can I make?”
Least common multiple (LCM) — The smallest number that is a multiple of two or more numbers. It answers “when will these line up again?”
Factor pair — Two factors that multiply to make a number. In a word problem, one is the number of groups and the other is the size of each group.
Prime factorization — Writing a number as a product of prime numbers, usually with a factor tree. Multiplying the primes two numbers share also gives the GCF.
Steps
The store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of each, with nothing left over — so the number of packs has to be a factor of BOTH quantities.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Listing them in order is what makes the comparison easy.
The numbers in both lists are the common factors: 1, 2, 3, 4, 6, and 12.
The greatest of those is 12, so the GCF of 48 and 36 is 12. The manager can make 12 combo packs — each holding 48 ÷ 12 = 4 pencils and 36 ÷ 12 = 3 notebooks.
Try it
Two supply runs repeat every 6 weeks and every 8 weeks, and both happen this week. When will they next happen in the same week?
Check your answer
Week 24, the least common multiple of 6 and 8
Repeating cycles land on multiples. Multiples of 6 are 6, 12, 18, 24 … and of 8 are 8, 16, 24 …, so the first shared week is 24 — the LCM.
Sentence starter
I know ___ because ___.
Goal: I can explain my choice using the words factor, multiple, common, greatest, and least.