HCF and LCM Formulae Examples

In this class, We discuss HCF and LCM Formulae Examples.

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1) Product of two numbers = product of their HCF and LCM.

Example:

HCF of two numbers is 11, and their LCM is 693.

If one of the numbers is 77, find the other.

Solution:

n1 and n2 are the numbers.

n1 * n2 = HCF * LCM

n2 = (11 * 693)/77

n2 = 99

other number = 99

2) Coprimes: Two numbers are said to be coprime if their HCF is 1.

Example:

Which of the following pair is coprime?

1) (16, 62) 2) (18, 25) 3) (21, 35) 4) (23, 72)

16, and 62 can be divided by 2

21, and 35 can be divided by 7

23 and 72 can be divided by 23

The coprime pair is 18, 25.

Example 3:

HCF of 3240, 3600, and a third number is 36. Their LCM is 2^4 * 3^5 * 5^2 * 7^2

Find the third number.

Solution:

From the basics:

HCF is the product of the lowest powers of common prime factors

LCM is the product of the highest power of all prime factors.

3240 = 2^3 * 3^4 * 5

3600 = 2^4 * 3^2 * 5^2

36 = 2^2 * 3^2

LCM = 2^4 * 3^5 * 5^2 * 7^2

Third number = 2^2 * 3^5 * 7^2

In HCF, we have 2^2. So 2^2 is missing in the remaining two numbers, so place it in the third number.

In LCM, we have 3^5, which is missing in the two numbers. So place in the third number.

Similarly, 7^2 in LCM

Example 4:

The ratio of the two numbers is 3: 4, and their HCF is 4. Find their LCM?

Solution:

The numbers are 3x and 4x.

In place of x, place the HCF value.

x= four why?

We can place six, and then the HCF of the two numbers will be 6.

So place x = 4.

Numbers are 3*4 = 12 and 4*4 = 16.

LCM(12, 16) = 48.