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Examoogle • User • info@examoogle.com • EE-2024-8821
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The smallest natural number which is divisible by 24, 6, 36 and 13 is:
1011
943
936
1008
936
Check divisibility: Since the number must be divisible by 36, it must also be divisible by 9 (sum of digits rule). Among options, only 936 has a digit sum of 18 (divisible by 9), while 1008 also has a sum of 9; check 13: 936/13=72, while 1008/13=77.53.
We are given four numbers: 24, 6, 36, and 13.
LCM(a,b,c,d)=∏pimax(ei)
Check divisibility: Since the number must be divisible by 36, it must also be divisible by 9 (sum of digits rule). Among options, only 936 has a digit sum of 18 (divisible by 9), while 1008 also has a sum of 9; check 13: 936/13=72, while 1008/13=77.53.
Students often calculate the LCM of only 24, 6, and 36, forgetting that 13 is a prime number and must be included as a factor.
Prime Factorization
Find the prime factors of each number: 24=23×31, 6=21×31, 36=22×32, and 13=131.
24=23×31,6=2×3,36=22×32,13=13
Determine LCM
The LCM is the product of the highest power of each prime factor present: 23 (from 24), 32 (from 36), and 131 (from 13).
LCM=23×32×13=8×9×13
Final Calculation
Perform the multiplication to find the smallest natural number.
8×9=72;72×13=936
C is correct because the Least Common Multiple of 24, 6, 36, and 13 is calculated to be 936.
This concept of finding the LCM is foundational for solving problems involving cyclic events, such as bells ringing at intervals or lights flashing at specific frequencies.
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