Page 60 - Start Up Mathematics_5

Example 26: Two lighthouses flash their lights every 20 seconds and 30 seconds respectively.
Given that they flashed together at 7 p.m., when will they next flash the lights
together?

Solution: To find the time of the next flash, let’s find the LCM of 20 seconds and
30 seconds.
2 20 , 30

2 10 , 15
5 5 , 15
3 1 , 3
1 , 1
LCM = 2 × 2 × 5 × 3 = 60

Thus, both lighthouses will flash together after every 60 seconds (or 1 minute).
Hence, the time when they will next flash together is 7:01 p.m.

EXERCISE 3.5

1. 210 green, 252 red and 294 orange balls are equally distributed among some students so
that no ball is left. What is the biggest possible number of students who got the balls?

2. Saumya has 12 sandwiches and 15 cookies. She wants to pack them to make identical
refreshment boxes. What is the greatest number of boxes that she can pack?

3. A bus service centre has 2 feed services that start together at 8 a.m. Bus A leaves at
15 minutes interval, while bus B leaves at 20 minutes interval. On a particular day, how
many times do both services leave together from 8 a.m. to 11 a.m.?
4. A group of students can be further separated into groups of 5, 13 and 17. What is the
smallest possible total number of students?

5. Rita goes to a shopping mall every 64 days. Archana goes to the same shopping mall
every 72 days. After how many days will they meet each other in the mall?

LET’S EVALUATE

1. Check the divisibility of the following numbers by 2, 3, 4, 5, 6, 8, 9, 10 and 11.
(a) 92,643 (b) 18,20,665 (c) 98,920 (d) 50,616 (e) 82,740 (f) 63,018

2. Check whether 225 and 169 are co-prime or not.
3. Find the HCF of the following numbers by long division method.

(a) 86 and 150 (b) 75 and 260 (c) 165, 350 and 425

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