5th Grade Relation Between
HCF and LCM
Here we will discuss about the relationship between hcf and lcm of two numbers.
Let us consider two numbers, 8 and 12.
8 = 2 × 2 × 2
12 = 2 × 2 × 3
|
L.C.M. = 2 × 2 × 2 × 3 = 24 The L.C.M. of 8 and 12 is 24. |
H.C.F. = 2 × 2 = 4 The H.C.F. of 8 and 12 is 4. |
The product of the L.C.M. and H.C.F. = 24 × 4 = 96
The product of the numbers, l.e., 8 × 12 = 96
We observe that the product of the numbers are the same as the product of the L.C.M. and H.C.F. of the numbers
Thus, for two numbers, we find the following relationship.
Product of two numbers = Product of H.C.F. and L.C.M. of the numbers.
Solved Examples on 5th Grade Relation Between HCF and LCM:
1. Find the product of H.C.F. and L.C.M. of 25 and 40.
Solution:
H.C.F. × L.C.M. = Product of two given numbers
Product of the given numbers = 25 × 40 = 1000
So, the product of H.C.F. and L.C.M. of 25 and 40 is 1000.
2. The L.C.M. of 84 and 108 is 756. Find the H.C.F.
Solution:
We know that,
H.C.F. × L.C.M. = Product of the numbers
H.C.F. = \(\frac{\textrm{Product of the numbers}}{\textrm{L.C.M.}}\)
= \(\frac{84 × 108}{756}\)
= 12
3. The product of two numbers is 1690 and their H.C.F. is 13. Find their L.C.M.
Solution:
We know that,
L.C.M. × H.C.F. = Product of the numbers
L.C.M. = \(\frac{\textrm{Product of the numbers}}{\textrm{H.C.F.}}\)
= \(\frac{1690}{13}\)
= 130
4. The L.C.M. of two numbers is 120. If their H.C.F. is 20 and one number is 40, find the other number.
Solution:
We know that,
H.C.F. × L.C.M. = One number × Other number
20 × 120 = 40 × Other number
2400 = 40 × Other number
Other number = \(\frac{2400}{40}\)
= 60
Therefore, the required other number is 60.
Worksheet on 5th Grade Relation Between HCF and LCM
1. Two numbers are 20 and 25. Calculate the product of their L.C.M. and H.C.F.
2. The product of two numbers is 4120. Their L.C.M. is 824. Find their H.C.F.
3. The product of two numbers is 5600. Their H.C.F. is 4. Find their L.C.M.
4. The L.C.M. of 576 and 128 is 1152. Find their H.C.F.
5. The H.C.F. of 186 and 496 is 62. Find their L.C.M.
6. The product of two numbers is 240. If their H.C.F. is 5 find their L.C.M
7. The product of two numbers is 450. If their L.C.M. is 75, find the H.C.F.
8. The HCF. of two numbers is 10 and their L.C.M. is 40. If the one number is 40, find the other number.
9. The LC.M. of two numbers is 125. If their product is 625, find their H.C.F.
10. The product of two numbers is 120. Find the product of the LC.M. and H.C.F. of the numbers
11. The product of H.CF. and L.C.M. of two numbers is 240. If one number is 24, find the other number.
12. The H.CF of two numbers is 5. If the product of the numbers is 375, find their LCM
13. The product of H.C.F. and L.C.M. of two numbers is 20. If one number is 4, find the other number.
14. The product of L.C.M. and H.C.F. of two numbers is 400. If one number is 25, find the other number.
Answer:
1. L.C.M. = 100; H.C.F. = 5
2. H.C.F. = 5
3. L.C.M. = 1400
4. H.C.F. = 64
5. L.C.M. = 1488
6. L.C.M. = 48
7. H.C.F. = 6
8. 10
9. 5
10. 120
11. 10
12. 75
13. 5
14. 16
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