LCM and HCF

Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next?

1. 7th January
2. 8th January
3. 12th January
4. 13th January

What is the LCM of x³ + 8, x² + 5x + 6 and x³ + 4x² + 4x?

1. x (x + 2)² (x + 3) (x² - 2x + 4)
2. x (x - 2)² (x - 3) (x² + 2x + 4)
3. (x + 2)² (x + 3) (x² - 2x + 4)
4. (x - 2)² (x - 3) (x² - 2x + 4)

The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?

1. p + q
2. p - q
3. pq
4. (pq)^-1

The sum of two positive integers is 52 and their LCM is 168. What is the ratio between the numbers?

1. 2 : 3
2. 5 : 4
3. 7 : 6
4. 7 : 8

What is the LCM of 2/3, 7/9, 14/15?

1. 14/3
2. 1/3
3. 2/3
4. 7/3

The product of two numbers is 6912 and their GCD is 24. What is their LCM

1. 296
2. 288
3. 286
4. 280

What is the HCF of 8(x⁵ - x³ + x) and 28(x⁶ + 1)?

1. (x⁴ + 1 - x²)
2. 4(x⁴ + 1 - x²)
3. 2(x⁴ + 1 - x²)
4. None

If for integer a, b and c if HCF(a,b) = 1 and HCF(a,c) = 1, then which one of the following is correct?

1. HCF(a,bc) = a
2. HCF(a,bc) = b
3. HCF(a,bc) = 1
4. None

What is the number of integral solutions of the equations HCF(a,b) = 5 and a + b = 65?

1. Exactly one
2. Infinitely many
3. Less than 65
4. None

In a fire range, four shooters are firing at their respective targets. The first, the second, the third and the fourth shooter hit the target once in every 5, 6, 7 and 8 seconds respectively. If all of them hit the target at 9:00 am, when will they hit their target together again.

1. 9:04 am
2. 9:08 am
3. 9:10 am
4. 9:14 am

Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

1. 75 m 60 cm
2. 50 m 40 cm
3. 25 m 20 cm
4. 75 m 60 cm

There are five hobby clubs in a college viz., photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?

1. 5
2. 3
3. 18
4. 10

Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.

1. 137
2. 140
3. 172
4. 1361

What is the greatest number which exactly divides 110, 154 and 242?

What is the highest 3 digit number which is exactly divisible by 3, 5, 6 and 7?