Question

The product of two numbers is 2160. If HCF is 12, find their LCM.​

Answer 1

Answer:

The product of two numbers is 2160 and their HCF is 12. What is their LCM?

The HCF is the Highest Common Factor or two numbers. Also know as the GCD - Greatest Common Divisor. The HCF/GCD of two numbers is the largest number that divides both of them. For example GCD of 20 and 28 is 4 and GCD of 98 and 56 is 14.

This is sort of the "brute force" method. Using what we know about prime factors we have

a∗b=2160

2160=2∗1080

2160=2∗2∗540

2160=2∗2∗2∗270

2160=2∗2∗2∗2∗135

2160=2∗2∗2∗2∗5∗27

2160=2∗2∗2∗2∗5∗3∗3∗3= 2160

Since the HCF is given as 12 then each number must contain 2∗2∗3

a=2∗2∗3

b=2∗2∗3

Looking at all the factors of 2160 we see we have used all of them except 3 and 5.

We must distribute the remaining factors , 3 and 5 between the two numbers which

can be done in the following two ways :

2∗2∗3∗3= 36

2∗2∗3∗5= 60

or

2∗2∗3= 12

2∗2∗3∗3∗5= 180

The LCM is the product of the most times you see any given factor in any of the

the prime factorization of the numbers. In either case above we find this the LCM is

2∗2∗3∗3∗5= 180

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Answer 2

Answer:

it's lcm is 180

Step-by-step explanation:

2160/12=180