the product of two numbers is 2160 and their hcf is 12 find there lcm
Answers
Answer:
Sorry l don't know the answer
Answer:
A calculation in mathematics say,
Product of two numbers is equal to the product of their HCF and LCM.
So if we take two numbers as a and b we have,
a x b= HCF(a,b) x LCM(a,b)
Thus,
2160 = 12 x LCM(a,b)
LCM(a,b) = 2160/12 =180
LCM(a,b) = 180
The question says, HCF is 12. This means both the numbers have 12 as a common factor which means the numbers can be
a = 12 x r …1
b = 12 x s …2
Where r and s are the numbers to which 12 is multiplied to get the original number. As per the question,
a x b = 2160
As per 1 and 2
12 x r x 12 x s = 2160
r x s = 15 …3
Now only 2 values are possible for r and s for 3 to be true,
r = 3, s = 5 or s = 3, r = 5
Let us take, r = 3, s = 5,
So, a = 12 x 3 = 36 b = 12 x 5 = 60
Now, 36 x 60 = 2160
HCF(36,60) = 12
LCM(36,60) = 180
So, the two numbers are 36 and 60
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