the gcf of two numbers is 3 and lcm is 180.if one of the numbers is 45,what is the other number?

the gcf of two numbers is 3 and lcm is 180.if one of the numbers is

45 = 3*3*5
180 = 2*2*3*3*5 <---- so the other number had to contain a factor of 2*2 or 4

also, let the other number has to be of the form 3k and it must contain a factor of 4, how about 12 ?

check: lcf of 12 and 45 is 3,
the lcm of 12 and 45 is ...
12 = 2*2*3
45 = 3*3*5
so we need: 2*2*3*3*5 = 180

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This is write answer

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That is correct explanation

180

We know that,
GCF(a,b) × LCM(a,b) = a × b
Substituting the values,
3 × 180 = 45 × b
= b = 3 × 180 ÷ 45
= b = 12
Therefore the other number is 12.
Hope it helped. =)

a=45
b=?
LCM=180
GCF=3
LCM (45,b)*GCF (45,b)=45,b
180*3=45,b
b=180*3÷45=12
good luck

Thanks for you ansewer

3×180=45+b
b=3×180÷45
b=12