Problems on HCF and LCM - Aptitude Questions Part 4

16. I want to stack the wooden blocks left after the carpentry work at home. I stack them in groups of 4 but 3 blocks get left out. So, I attempt with stacks of 5 blocks each but again 3 blocks remain left out. The same thing happens even when I try with 9 blocks and 10 blocks in each stack. Find the total number of blocks I have.

a. 90
b. 180
c. 183
d. 900

Answer: c. 183

Explanation:

Since we need total number of blocks, we must first find LCM of 4, 5, 9, 10
-------------------------------------------------
2           4           5           9           10
-------------------------------------------------
5           2           5           9           5
             2           1           9           1
-------------------------------------------------
∴ LCM = 2 x 5 x 2 x 1 x 9 x 1 = 180

Since remainder is same i.e. 3 blocks in each case, just add it to this LCM
Number of blocks = 180 + 3 = 183


17. A pattern is formed with six type of LEDs. They start lighting together and then light at intervals of 2, 4, 6, 8, 10 and 12 seconds, respectively. In half an hour, how many times do they light together?

a. 4
b. 10
c. 15
d. 16

Answer: d. 16


18. Find the largest of following fractions.

a. 63/80
b. 31/40
c. 13/16
d. 7/8

Answer: d. 7/8


19. Find the smallest number which when reduced by 7, can be perfectly divided by 12, 16, 18, 21 and 28 each.

a. 1008
b. 1015
c. 1022
d. 1032

Answer: a. 1008


20. A and B are two primes numbers, A > B. Their LCM is 161. Find the value of 3B - A :

a. -2
b. -1
c. 1
d. 2

Answer: a. -2

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