If the H.C.F. of two numbers is 1 and their L.C.M. is 36, what can be said about
Practice Questions
Q1
If the H.C.F. of two numbers is 1 and their L.C.M. is 36, what can be said about the two numbers?
They are co-prime
They are equal
They are both even
They are both odd
Questions & Step-by-Step Solutions
If the H.C.F. of two numbers is 1 and their L.C.M. is 36, what can be said about the two numbers?
Step 1: Understand what H.C.F. means. H.C.F. stands for Highest Common Factor, which is the largest number that divides both numbers without leaving a remainder.
Step 2: Understand what L.C.M. means. L.C.M. stands for Lowest Common Multiple, which is the smallest number that both numbers can divide into without leaving a remainder.
Step 3: Note that the H.C.F. of the two numbers is given as 1. This means that the only common factor between the two numbers is 1.
Step 4: Since the H.C.F. is 1, it indicates that the two numbers do not share any other factors. This means they are co-prime.
Step 5: The L.C.M. of the two numbers is given as 36. This is the smallest number that both numbers can multiply into.
Step 6: Conclude that since the H.C.F. is 1, the two numbers are co-prime, meaning they have no common factors other than 1.
H.C.F. and L.C.M. – Understanding the relationship between the highest common factor (H.C.F.) and the least common multiple (L.C.M.) of two numbers, particularly that if H.C.F. is 1, the numbers are co-prime.
Co-prime Numbers – Co-prime numbers are pairs of numbers that have no common factors other than 1.
