What is the greatest common factor anf least common multiple of 36 and 45?

Answer 1

The LCM of these is the lowest whole number which is evenly divisible by all the numbers. It is the smallest number which is a common (i.e. a shared) multiple of all the numbers.

The answer is 360. This is because, starting at 0 and then looking at every following positive integer (whole number), 360 is the first (i.e. the lowest) number which divides evenly by all the other numbers.

A factor of a number is a positive whole number which evenly divides into the number. So, for example, 1 will always be a factor of every number. If we write down (in descendingorder) all the factors of one of the numbers (often it is easiest to pick the smallest number, but not always) then we can look at each in turn and ask which of these is the first common (shared) factor.

The factors of 10 are 10,5,2 and 1. The first number here which is also a factor of both 24 and 45 is 1. Therefore the greatest common factor (indeed the only common factor) is 1.

Answer 2

The GCF of 32 and 45 is 1.

The LCM of 32 and 45 is 1440.

Answer 3

Using prime factorisation:

36 = 2² x 3²

45 = 3² x 5

→hcf = 3² = 9

→lcm = 2² x 3² x 5 = 180

Answer 4

2 x 2 x 3 x 3 = 36

3 x 3 x 5 = 45

3 x 3 = 9, the GCF

2 x 2 x 3 x 3 x 5 = 180, the LCM

Check it.

36 x 45 = 1620

180 x 9 = 1620

It checks.

Answer 5

The GCF is 9.

The LCM is 180.

Answer 6

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