If the product of two co-prime numbers is 783, then find the L.C.M. of these…
2023
If the product of two co-prime numbers is 783, then find the L.C.M. of these numbers.
- A.
1
- B.
783
- C.
L.C.M will be equal to H.C.F
- D.
None of these
Attempted by 5 students.
Show answer & explanation
Correct answer: B
To solve this problem, you need to understand the relationship between co-prime numbers, their Highest Common Factor (H.C.F.), and their Least Common Multiple (L.C.M.).
The Mathematical Principle
Definition of Co-prime Numbers: Two numbers are co-prime (or relatively prime) if their only common factor is 1. This means their H.C.F. is always 1.
Relationship between H.C.F. and L.C.M.: For any two numbers, the product of the two numbers is equal to the product of their H.C.F. and their L.C.M.
Product of numbers = H.C.F. × L.C.M.Application to Co-primes: Since the H.C.F. of co-prime numbers is 1, the formula simplifies to:
Product of numbers = 1 × L.C.M.
Therefore, L.C.M. = Product of the two numbers.
Step-by-Step Calculation
Given: Product of two co-prime numbers = 783.
Based on the principle above, for co-prime numbers, the L.C.M. is identical to their product.
Therefore, the L.C.M. = 783.