Question 7 of 18intermediate💡 UnderstandShort Answer2 marks
The LCM of 3 and 24 is 24 (it is one of the two given numbers). (a) Find more such number pairs where the LCM is one of the two numbers. (b) Make a general statement about such numbers. Describe such number pairs using algebra.
(a)
Find more number pairs where LCM is one of the numbers
Answer
(2, 6), (4, 12), (5, 15), (7, 21), (3, 9)
(b)
Make a general statement using algebra
Answer
If n and m×n are two numbers, LCM(n, m×n) = m×n. This happens when one number is a factor of the other.
Explanation
(a) In each pair, the smaller number divides the larger number. (b) The larger number contains all prime factors of the smaller, making it the LCM.