## Finding HCF & LCM with Prime Factorizations

We want to find the HCF and LCM of the numbers 60 and 72.

Start by writing each number as a product of its prime factors.

60 = 2 * 2 * 3 * 5 |

72 = 2 * 2 * 2 * 3 * 3 |

60 | = 2 | * 2 | * 3 | * 5 | ||

72 | = 2 | * 2 | * 2 | * 3 | * 3 |

appear in

__both__lists:

So the HCF of 60 and 72 is

**2 × 2 × 3**which is

**12**.

The lowest common multiple is found by multiplying all the factors which appear in

__either__

__list:__

So the LCM of 60 and 72 is

**2 × 2 × 2 × 3 × 3 × 5**which is

**360**.