23. Find the least number of five digits that is exactly divisible by 16 , 18,24 and 30
24. Find the greatest number of five digits exactly divisible by 9. 12. 15, 18 and 24.
25. Three bells toll at intervals of 9. 12. 15 minutes. If they start tolling together, after what time
will they next toll together?
Answers
Answer:
24. 720
L.C.M of 16, 18, 24, and 30 is 720. 720 is only a 3 digit number. But we have to find the least five digit number. So we must multiply 720 by the smallest integer that will make it be at least 10000, which is the smallest 5-digit number.
25. Greatest number of five digits divisible by 9, 12, 15, 18 and 24 = 99999 - 279 = 99720. Sol: LCM of 9, 12, 15, 18 and 24 by division method is 360. The quotient when 99999 is divided by 360 is 277 and the remainder is 279.
26.This problem based on the concept of LCM.
Here we have to find LCM of intervals 9 , 12 , 15 minutes which indicates after how long they all again toll together.
Write 9 , 12 and 15 product of prime factors,
9 = 3 × 3
12 = 2 × 2 × 3
15 = 3 × 5
LCM( 9 , 12 , 15 ) = 3 × 3 × 2 × 2 × 5
= 180
Three bell toll together after 180
minutes .
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Answer:
23) 810
24)699,840
25)13min