H.C.F. of two numbers divides their L.C.M. exactly. Since 16 is not a factor of 136, it states that there does not exist any pair of numbers with H,C.F. 16 and L.C.M. 136.

Correct Option: D

H.C.F. of two numbers divides their L.C.M. exactly. Since 16 is not a factor of 136, it states that there does not exist any pair of numbers with H,C.F. 16 and L.C.M. 136.

The least common multiple of 38 and 57 is 114 and the multiple which is between 900 and 1000 is 912.

Now, 912 + 23 i,e 935 lies between 900 and 1000 and when divided by 38 and 57 leaves in each case 23 as the remainder.

Therefore, 935 is number required.

Correct Option: A

The least common multiple of 38 and 57 is 114 and the multiple which is between 900 and 1000 is 912.

Now, 912 + 23 i,e 935 lies between 900 and 1000 and when divided by 38 and 57 leaves in each case 23 as the remainder.

Therefore, 935 is number required.

From the question we see that the second number is a common factor of the two products and since the numbers are prime to one another. It is their . H. C. F . and is, therefore, 19.

∴ The first number = 437 / 19 = 23
and the third number = 551 / 19 = 29
Hence, the number are 23, 19 and 29
∴ Sum = 23 + 19 + 29
= 71.

Correct Option: C

From the question we see that the second number is a common factor of the two products and since the numbers are prime to one another. It is their . H. C. F . and is, therefore, 19.

∴ The first number = 437 / 19 = 23
and the third number = 551 / 19 = 29
Hence, the number are 23, 19 and 29
∴ Sum = 23 + 19 + 29
= 71.

The L.C.M of 9, 10, 15 = 90
On dividing 1936 by 90, the remainder = 46
But a part of this remainder = 7
Hence, the two numbers = 46 - 7 = 39.

Correct Option: C

The L.C.M of 9, 10, 15 = 90
On dividing 1936 by 90, the remainder = 46
But a part of this remainder = 7
Hence, the two numbers = 46 - 7 = 39.

Find the H.C.F. of 84 and 180, which is 12 and this is the required answer .

Correct Option: D

Find the H.C.F. of 84 and 180, which is 12 and this is the required answer .