HCF AND LCM-01

Question: Four bells commence tolling together, they tall at intervals of 1, 1 ¼, 1½ and 1¾ seconds respectively, after what interval will they tall together again? [चार घंटियाँ क्रमशः1, 1 ¼, 1½ तथा 1¾ सेकेण्ड के अन्तराल पर बजती हैं. वे चारो एक साथ कब बजेंगी?]  [Ans. (d) 1 minutes 45 sec]

(a) 2 min. 40 sec (b )1 min. 40 sec (c) 2 min. 45 sec (d) 1 min 45 sec (e) none of these

Solution:

Detailed Explanation: The least number, which is divisible by each of the given numbers 1, 1 ¼, 1½ and 1¾; that is, their LCM. This LCM is the length of interval, when all the bells tall together.

LCM of 1, 1 ¼, 1½ and 1¾ = LCM of (1/1), (5/4), (3/2) and (7/4)

 = (LCM of 1, 5, 3, 7)/HCF of (1, 4, 2, 4)

= (105/1) = 105 sec = 1 min 45 sec. Ans.