question_answer 1)

Find the LCM of the following numbers (a) 9 and 4                           (b) 12 and 5                        (c) 6 and 5                           (d) 15 and 4 Observe a common property in the obtained LCM. Is LCM the product of two numbers in each case?

Answer:

                (a) LCM of 9 and 4 2 9, 4 2 9, 2 2 9, 1 3 3, 1 1, 1 \[\therefore \] LCM\[=2\times 2\times 3\times 3=36\] (b) LCM of 12 and 5 2 12, 5 2 6, 5 2 3, 5 5 1, 5 1, 1 \[\therefore \] LCM\[=2\times 2\times 3\times 5=60\] (c) LCM of 6 and 5 2 6, 5 3 3, 5 5 1, 5 1, 1 \[\therefore \] LCM\[=2\times 3\times 5=30\] (d) LCM of 15 and 4 2 15, 4 2 15, 2 3 15, 1 5 5, 1 1, 1 \[\therefore \] LCM \[=2\times 2\times 3\times 5=60\] Here, we see that in each case LCM of given numbers is a multiple of 3 and 2. Yes, in each case LCM = Product of two given numbers.