Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Which of the following numbers is divisible by all the natural numbers from 1 to 10 (both inclusive)?
1000
2520
504
608
2520
Check divisibility rules: The number must be divisible by 9 (sum of digits is a multiple of 9) and 8 (last three digits divisible by 8) and 7 (multiple of 7).
Find the smallest number divisible by all natural numbers from 1 to 10 (both inclusive).
LCM(1,2,3,4,5,6,7,8,9,10)=23├Ч32├Ч51├Ч71
Check divisibility rules: The number must be divisible by 9 (sum of digits is a multiple of 9) and 8 (last three digits divisible by 8) and 7 (multiple of 7).
Confusing 'divisible by' (LCM) with 'divisor of' (HCF) or incorrectly assuming 1000 is divisible by 7 or 9.
Prime factorization of numbers 1 to 10
List the prime factorizations for each number: 1=1, 2=21, 3=31, 4=22, 5=51, 6=21├Ч31, 7=71, 8=23, 9=32, 10=21├Ч51.
23,32,51,71
Calculate the Least Common Multiple (LCM)
To find the LCM, take the highest power of each prime factor present in the set: 23, 32, 51, and 71.
LCM=8├Ч9├Ч5├Ч7
Perform final multiplication
Calculate the product: 8├Ч9=72, 72├Ч5=360, and 360├Ч7=2520.
360├Ч7=2520
B is correct because the Least Common Multiple of all integers from 1 to 10 is 2520, which is exactly divisible by all of them.
This concept is fundamental for time-based problems, such as finding when multiple periodic events (like ringing bells or blinking lights) will coincide again.
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 тАв 100K+ Aspirants