^{_{Find the rod of the greatest length which can measure exactly 42m,49m and 63m.}}

The Length of the largest rod  which can measure 42 m, 49 m and 63 m exactly is the HCF of 42 m, 49 m and 63 m.

Prime factorization of 42 = 2 × 3 × 7.

Prime factorization of 49 = 7  × 7.

Prime factorization of 63 = 3 × 3 × 7.

HCF of 42, 49 and 63 = 7

Thus, the length of the longest rod which can measure 42 m, 49 m and 63 m exactly is 7 m.