Word Problem Involving the Least Common Multiple of 2 Numbers Online Quiz

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Q 1 - Determine the smallest 3-digit number which is exactly divisible by 12 and 20

Answer : B

Explanation

Step 1:

The multiples of 12 and 20 are

12, 24, 36, 48, 60…

20, 40, 60...

Step 2:

So the lcm of 12 and 20 is 60. The multiples of 60 are 60, 120, 240…

Step 3:

The smallest 3-digit number which is exactly divisible by 12 and 20, is therefore 120.

Q 2 - There are less than 10 dozen eggs in a large basket. If you count them 3, 5, or 7 at a time, there are none left over. How many eggs are in the basket?

Answer : C

Explanation

Step 1:

3, 5 and 7 are prime numbers.

Step 2:

So the lcm of 3, 5 and 7 is = 3 × 5 × 7 = 105

So there are 105 eggs in the basket.

Q 3 - Two persons start off together for a morning walk. Their steps measure 45 cm and 60 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

Answer : D

Explanation

Step 1:

The required distance is given by the lcm of 45 and 60.

The multiples of 45 and 60 are

45, 90, 135, 180…

60, 120, 180…

Step 2:

Therefore, the lcm of 45 and 60 is 180 cm.

Q 4 - Find the greatest number of 4-digits which is exactly divisible by 48 and 72.

Answer : B

Explanation

Step 1:

The multiples 48 and 72 are

48, 96, 144

72, 144

Step 2:

Therefore, the lcm of 48 and 72 is 144

The multiples of 144 are 144, 288…9936

Step 3:

So the greatest number of 4-digits divisible by 48 and 72 is 9936.

Q 5 - Jose wishes to promote his business, so he distributes packs of 15 yellow flyers and sets of 17 blue flyers. In the evening, Jose finds that he distributed the same number of yellow and blue flyers. What is the minimum number of flyers of each color?

Answer : A

Explanation

Step 1:

The required number is found by calculating the lcm of 15 and 17.

Step 2:

The lcm of 15 and 17 is 15 × 17 = 255.

Q 6 - Two bells ring once at the same time. After that, the first bell rings after every 63 minutes, and the second after every 42 minutes. After how many minutes will they again ring together?

Answer : C

Explanation

Step 1:

The first bell rings after 63 minutes

The second bell rings after 42 minutes

The multiples of 63 and 42 are

42, 84, 126…

63, 126…

Step 2:

So, the lcm of 63 and 42 is 126

The two bells will ring again after 126 minutes

Q 7 - Ricky strikes the drums every 10 seconds and the cymbals every 16 seconds. If he just struck both at the same time, how many seconds will pass before he again strikes them at the same time?

Answer : D

Explanation

Step 1:

Ricky strikes drums every 10 seconds

Ricky strikes cymbals every 16 seconds

The multiples of 10 and 16 are

10, 20, 30…80…

16, 32, 64, 80…

Step 2:

So, the lcm of 10 and 16 is 80

Ricky strikes the drums and cymbals again after 80 seconds.

Q 8 - The traffic lights at two road junctions change after every 91 seconds and 117 seconds respectively. If they change simultaneously now, after how many seconds will they change simultaneously again?

Answer : C

Explanation

Step 1:

The multiples of 91 and 117 are

91, 182...819

117, 234…819

Step 2:

The lcm of 91 and 117 is 819 seconds.

The traffic lights will change after 819 seconds.

Q 9 - Bill and Stella start at the same time in the same direction to run around a stadium. Bill completes a round in 144 seconds and Stella in 192 seconds, both starting at the same point. After what time will they meet again at the starting point?

Answer : B

Explanation

Step 1:

The multiples of 144 and 192 are

144, 288, 432, 576…

192, 384, 576…

Step 2:

So, the lcm of 144 and 192 is 576.

Bill and Stella will meet after 576 seconds.

Q 10 - Natalie is buying pencils (pack of 17) and pens (pack of 12) from the store. If Natalie wishes to purchase the same number of pencils as pens, what is the smallest number of pens that she can buy?