The least number which, when diminished by 9, is divisible by 13, 20, 10 and 23 is:
Solution:
The prime factorization of each number:
13 = 13
10 = 2 × 5
23 = 23
The LCM is found by taking the highest powers of all primes involved:
Calculate the LCM
LCM = 4 × 5 × 13 × 23
LCM = 20 × 13 = 260
LCM = 260 × 23 = 5980
Find the Least Number
The least number which, when diminished by 9, is divisible by 13, 20, 10, and 23, is:
Least number = LCM + 9 = 5980 + 9 = 5989
The least number is 5989.
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