What is the lowest common multiple and the highest common factor of 120 and 150?

To approach a problem like this, we must first break down our number into a multiplication of prime factors (i.e. we can make our number by multiplying numbers 2,3,5,7 etc together). This is best done with a factor tree and gives the result below120 = 2 x 60 = 2 x 2 x 30 = 2 x 2 x 2 x 15 = 2 x 2 x 2 x 3 x 5150 = 3 x 50 = 3 x 2 x 25 = 3 x 2 x 5 x 5Now we have the number in prime factor form, we can find HCF (highest common factor) and the LCM (lowest common multiple)It's important to remember... a factor of a number is a number that when multiplied by an integer makes that number A multiple of a number is a number that can be made by multiplying the number by an integerHCFFor the HCF, we must multiply the prime factors appearing in both the prime factor forms of our numbers 120 = 2 x 2 x 2 x 3 x 5150 = 3 x 2 x 5 x 5So HCF = 2 x 3 x 5 = 30note: we only have one 2 here as 150 only has one 2 as a prime factorit can be useful to circle numbers pairs of numbers from both listsLCMFor the LCM, we must multiply the HCF by all the prime factors that couldn't be paired up in calculating the HCF This is easy to visualise if you circle pairs of numbers appearing in both the numbers prime factor form when you are calculating HCF120 = 2 x 2 x 2 x 3 x 5150 = 3 x 2 x 5 x 5so LCM = 2 x 3 x 5 x 2 x 2 x 5 = 600