Relation between HCF and LCM
Relation between HCF and LCM is stated below:
Product of two numbers is equal to product of their LCM and HCF, i.e.
(HCF of Two Numbers) × (LCM of Two Numbers) = Product of two Numbers
For example: 10 and 11 are coprime numbers.
- 10 = 1 × 1
- 11 = 1 × 11
LCM of 10 and 11 = 110
HCF of 10 and 11 = 1
Product of 10 and 11 = 10 × 11 = 110
Consider two numbers A and B, then
Therefore, LCM (A , B) × HCF (A , B) = A × B
Special Cases Of HCF And LCM
When dealing with rational numbers, understanding the rules and ratios of HCF and LCM is crucial. In cases where more than two numbers are involved, the process remains the same.
By multiplying the numbers and their HCF, and dividing them by their respective pairs’ HCF, we can calculate the LCM.
The same applies when finding the HCF, using the LCM in place of the HCF in the formula.
Consequently,
LCM = (x×y×z) × (HCF of x, y, z)/ HCF (x, y) × HCF (y, z) × HCF (x, z)
To find the HCF, the inverse formula needs to be used.
HCF (x,y and z) = (x×y×z) × (LCM of x, y, z)/ LCM (x, y) × LCM (y, z) × LCM (x, z)
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Relation between HCF and LCM
Lowest Common Multiple (LCM) and the Highest Common Factor (HCF), are closely connected. They play a key role in simplifying mathematical statements, prime factorization, and finding relationships between numbers, especially when dealing with fractions. To understand the relationship between the HCF and LCM of two or more numbers, one must grasp the concepts of LCM and HCF and know how to apply the relevant formulas.
HCF and LCM Relation
This article provides a detailed explanation, with examples, to clarify the connection between the HCF and LCM values given.