GCF and LCM · part 1 of 7
The Vocabulary
The five words inside the two names, plus prime. Start here.
Read the words before you do any maths
Start with prime, the word you need all the way through. Then the two names, which are three words stuck together, one word at a time.
primea whole number bigger than 1 that nothing divides into except 1 and itself. 2, 3, 5, 7, 11, 13, 17, and on forever. Those are only the first few: 29 is prime, and so is 101.
factora number that divides into it evenly, with nothing left over. 3 is a factor of 12.
multiplea number you land on counting up by it. 12 is a multiple of 3.
commonboth numbers have it.
greatestthe biggest one of those.
leastthe smallest one of those.
Greatest common factor reads as: the biggest number that divides evenly into both of them.
Least common multiple reads as: the smallest number that both of them divide evenly into.
Notice they point opposite ways. A factor is smaller than the number, or equal to it. A multiple is bigger than the number, or equal to it. So the GCF can never be bigger than the smaller of your two numbers, and the LCM can never be smaller than the bigger one. That one sentence catches most wrong answers.