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.
Common factor — A factor that two numbers both have.
Greatest common factor — The largest factor two numbers share.
Least common multiple — The smallest multiple two numbers share.
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
At home, the dog gets a bath every 4 weeks and the cat gets its medicine every 6 weeks, and both happen this week. When will they next happen in the same week?
Check your answer
Week 12, the least common multiple of 4 and 6
Repeating cycles land on multiples. Multiples of 4 are 4, 8, 12 … and of 6 are 6, 12 …, so the first shared week is 12 — the LCM.
Sentence starter
I know ___ because ___.
Goal: I can explain my choice using the words factor, multiple, common, greatest, and least.