Two machines need to be oiled at intervals of 12 and 18 days. What is the least number of days after which they will need to be oiled together again?(a) 6 days(b) 12 days(c) 18 days(d) 36 days
Question
Two machines need to be oiled at intervals of 12 and 18 days. What is the least number of days after which they will need to be oiled together again?(a) 6 days(b) 12 days(c) 18 days(d) 36 days
Solution
The least number of days after which the two machines will need to be oiled together again is determined by finding the least common multiple (LCM) of the two intervals, 12 and 18 days.
Step 1: List the prime factors of each number.
- Prime factors of 12: 2, 2, 3
- Prime factors of 18: 2, 3, 3
Step 2: Multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply it the greatest number of times it occurs.
- 2 occurs twice in 12 and once in 18, so you multiply by 2 twice.
- 3 occurs once in 12 and twice in 18, so you multiply by 3 twice.
Step 3: Multiply the results from step 2 to get the LCM.
- 2 * 2 * 3 * 3 = 36
So, the least number of days after which they will need to be oiled together again is 36 days. Therefore, the answer is (d) 36 days.
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