Calculate the smallest five-digit number divisible by 9, 11 and 21.
Given:
Numbers: 9, 11, and 21
Solution:
LCM of 9, 11, and 21:
Prime factorization:
9 = 3²
11 = 11
21 = 3 × 7
LCM = Highest powers of all prime factors = 3² × 7 × 11
LCM = 9 × 7 × 11 = 693
To find the smallest five-digit number divisible by 693:
Smallest five-digit number = 10000
Divide 10000 by 693:
10000 ÷ 693 = 14.43 (approximately)
Take the next whole number greater than 14.43, which is 15.
Smallest five-digit number divisible by 693 = 693 × 15 = 10395
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