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.