Question

The lcm of 2 number of 3 digit each 1740 and hcf is 290 then two number are

Answer 1

The numbers are 580 and 870.

Step-by-step explanation:

Given LCM of two numbers is 1740 and HCF is 290.

The product of two numbers = LCM x HCF = 1740 x 290 = 504600

The numbers must be multiples of HCF. So, let the numbers be 290a and 290b where a and b are two numbers prime to each other.

290a x 290b = 504600

=> ab = 6

Now, the pairs of numbers whose product is 6 are (1, 6) and (2, 3)

Required numbers are  1 x 290 = 290 and 6 x 290 = 1740

                                         2 x 290 = 580 and 3 x 290 = 870

Given that both the numbers are 3 digits so answer cannot be 290 and 1740.

Hence, the numbers are 580 and 870.