Find two possible pairs of numberssuch that the HCF and L.C.M ofeach p

1.	Find two possible pairs of numberssuch that the HCF and L.C.M ofeach pair of numbers are 21 and630, respectively.
Answer» LCM and HCF of two numbers are given we have to find the numbers. Let HCF of two numbers be 21 and LCM be 630. Let numbers be x and y. x = 21a and y=21b, where a and b are relative prime to each others. 21ab = LCM of x and y ab = 630/21 = 30 Now find a and b relative prime to each others and ab=30. Thus (1,30), (2,15), (3, 10), (5, 6). The possible numbers are (21, 630), (42, 315), (63, 210), (105, 126).

Find two possible pairs of numberssuch that the HCF and L.C.M ofeach pair of numbers are 21 and630, respectively.

Answer»

LCM and HCF of two numbers are given we have to find the numbers.

Let HCF of two numbers be 21 and LCM be 630.

Let numbers be x and y.

x = 21a and y=21b, where a and b are relative prime to each others.

21ab = LCM of x and y

ab = 630/21 = 30

Now find a and b relative prime to each others and ab=30.

Thus (1,30), (2,15), (3, 10), (5, 6).

The possible numbers are (21, 630), (42, 315), (63, 210), (105, 126).