CPO 2019 23-11-2020(Evening Shift)
(a) 240
(b) 180
(c) 150
(d) 120
Answer: 120
To solve this problem, we need to find the least common multiple (LCM) of the numbers 5, 6, 8, 10, and 12. The LCM of a set of numbers is the smallest positive integer that is divisible by each of the numbers in the set.
Here are the steps to find the LCM:
1. First, we need to find the prime factorization of each number.
- The prime factorization of 5 is 5.
- The prime factorization of 6 is 2 * 3.
- The prime factorization of 8 is 2^3.
- The prime factorization of 10 is 2 * 5.
- The prime factorization of 12 is 2^2 * 3.
2. Next, we take the highest power of each prime number from the factorizations.
- The highest power of 2 is 2^3 from the factorization of 8.
- The highest power of 3 is 3 from the factorization of 6.
- The highest power of 5 is 5 from the factorization of 5 or 10.
3. Finally, we multiply these highest powers together to get the LCM.
- LCM = 2^3 * 3 * 5 = 8 * 3 * 5 = 120.
So, the least number which is exactly divisible by 5, 6, 8, 10 and 12 is 120.
Answer: 120
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