Highest Common Factor And Least Common Multiple MCQ Set 7

Showing question 31 to 35 of total 54 MCQs

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Question No: 31

3 birds fly along the circumference of a jungle. They complete one round in 27 minutes, 45 minutes and 63 minutes respectively. Since they start together, when will they meet again at the starting position?

1. 945 minutes
2. 126 minutes
3. 135 minutes
4. 9 hours

Answer: A

Explanation

We need the next instance that means the LCM of times of all 3 birds.

LCM = 9 × 3 × 5 × 7 =945 = They meet after 945 minutes.

Question No: 32

What least possible 4-digit number, when divided by 12, 16, 18 and 20 leaves 21 as remainder?

1. 36
2. 133
3. 144
4. 1461

Answer: D

Explanation

Here least possible 4 digit number is needed that means we need the LCM

We must first find LCM of 12, 16, 18 and 20.

LCM = 2 × 3 × 2 × 1 × 4 × 3 × 5 = 720

Now this is a 3 digit number.

But 1440 is divisible by 12,16,18 and 20.

So, Number = 1440 + 21 = 1461.

Question No: 33

5 clocks ring automatically at intervals of 12 minutes, 8 minutes, 3 minutes, 4 minutes and 10 minutes, respectively. In 8 hours from the moment they start, how many times will they ring together?

1. 12 times
2. 5 times
3. 3 times
4. 4 times

Answer: D

Explanation

We need the next instances when the alarm rings.

That means the Least common Multiple (LCM) of 3,4,8,10,12

3,4 divide 12 so neglect them.

LCM of 8, 10 and 12

After starting, they ring together First time in 2 hours.

The second time in 2 + 2 = 4 hours

Then third time in 6 hours.

And fourth time in 8 hours.

Question No: 34

What least number when divided by 36, 24 and 16 leaves 11 as remainder in each case?

1. 36
2. 133
3. 144
4. 155

Answer: D

Explanation

Here least number is needed that means we need the LCM

we must first find LCM of 36, 24 and 16

LCM = 4 × 3 × 2 × 2 × 1 × 3 = 144

Since remainder is same just add it to this LCM

Number = 144 + 11 = 155

Question No: 35

If (x - 4) is the HCF of x² - 8x + 15 and x² - kx +1 , then what is k?

1. 8/15
2. 4
3. 5
4. 15/8