What is the largest 4-digit number divisible by 3, 7, 11 and 13?

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

Find the smallest number which when divided by 12, 18 and 24 leaves remainder 5 in each case.

The HCF and LCM of two numbers p and q are 44 and 4620 respectively. When p is divided by 55, the quotient is 4 and remainder is 0. What is the value of q?

Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:

If HCF of 768 and x⁶y² is 32xy for natural numbers x ≥ 2, y ≥ 2, then what is the value of (x + y )?