2929.The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
1008
1015
1022
1032
Explanation:
Required number = L.C.M. of $\left(12,16, 18, 21, 28\right)$ + 7
= 1008 + 7
= 1015
2930.Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
4
10
15
16
Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds [2 minutes].
In 30 minutes, they will toll together$ \dfrac{30}{2} $+ 1 = 16 times.
2932.252 can be expressed as a product of primes as:
2 x 2 x 3 x 3 x 7
2 x 2 x 2 x 3 x 7
3 x 3 x 3 x 3 x 7
2 x 3 x 3 x 3 x 7
Explanation:
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
2933.The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
123
127
235
305
Explanation:
Required number = H.C.F. of $\left(1657 - 6\right)$ and $\left(2037 - 5\right)$