Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
The smallest six-digit natural number that is exactly divisible by 8, 10, 12 and 16 is:
100020
100040
100060
100080
100080
Find the LCM of 8, 10, 12, 16. The LCM is 240. Divide the smallest 6-digit number (100000) by 240 and add the remainder difference to the next multiple.
Divisors: 8, 10, 12, 16. Target: Smallest 6-digit natural number.
LCM(a,b,c,d)=Smallest common multiple, Target=Smallest 6-digit number+(LCM−(Smallest 6-digit number%LCM))
Find the LCM of 8, 10, 12, 16. The LCM is 240. Divide the smallest 6-digit number (100000) by 240 and add the remainder difference to the next multiple.
Students often pick the smallest number divisible by the LCM rather than finding the smallest 6-digit number, or forget that the remainder needs to be adjusted up to the next multiple of 240.
Find the LCM of 8, 10, 12, and 16
Prime factorizations: 8=23, 10=2×5, 12=22×3, 16=24. Taking the highest powers: 24×31×51=16×3×5=240.
LCM(8,10,12,16)=240
Divide the smallest 6-digit number by the LCM
The smallest 6-digit number is 100000. Divide 100000 by 240. 100000÷240=416.666...
100000=416×240+160
Calculate the smallest 6-digit multiple
To get the next multiple of 240, calculate 240−160=80. Add this difference to 100000. 100000+80=100080
100080
D is correct because 100080 is the smallest 6-digit natural number divisible by the LCM of 8, 10, 12, and 16, which is 240.
This logic is essential for 'Bell Ringing' or 'Circular Track' problems where multiple events must synchronize at a specific time.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants