Question

The LCM of two numbers is 210 and their HCF is 14. How many such pairs are possible?

Answer 1

two(2) pair are soluble

Answer 2

If, suppose the two numbers are a and b and their LCM is x and their HCF is y then, a × b = x × y

Now, The LCM of two numbers is 210 and their HCF is 14.

so, x * y = 210 * 14 = 2940

Now, 2940 = 14 * 210

                   = 28 * 105

                   = 42 * 70

                   = 35 * 84

                   = 30 * 98

                   = 140 * 21

                   = 196 * 15

From this pairs, we can find  the possible pairs easily just calculating their LCM and HCF. So, the possible pairs will be (14, 210), (42, 70). This two pairs are the possible pairs.(ans.)