divisible problems 3

what is the least positive number that is divisible by the first 10 positive integers(1,2,3,4,5,6,7,8,9,10)?


The answer is 2520.

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7 solutions

Rishi Hazra
Nov 4, 2014

first of all, note down the prime factors which are 2,3,5,7

2 * 3 * 5 * 7 ..................................as prime factors are absolutely indispensable

for 8 to be able to divide the number, 4 must be multiplied to it

thus we get

2 * 3 * 5 * 7 * 4 ..................................hence 4 will also divide the number now

6 and 10 already divides the number.............( see divisibility rule for 6)

for 9, one more 3 must be multiplied

thus the answer is 2 * 3 * 5 * 7 * 4 * 3 = 2520

nice solution

math man - 6 years, 7 months ago
Arjun Sanyal
Apr 21, 2015

7 × 8 × 9 × 5 = 2520 8 takes care of 2, 4 and 8; 9 takes care of 3. Since 2 and 3 are considered already, 6 is taken care of. Taking 5 to also factor in 10, since 2 already considered

Fox To-ong
Dec 21, 2014

using LCM: 2^3 X 3^3 X 5 X 7 = 2520

Harshita Moondra
Nov 24, 2014

find the LCM or multiply 7,8,9,5(2 2 2 3 3 5 7) because the LCM of 2,4,8 is 8 and that of 3,9 is 9 and when you multiply them the you get the LCM of 2,3,4,6,8,9. Then you just need to multiply 5 and 7. therefore the ans will be 2^3 3^2 5*7=2520

Sunil Pradhan
Nov 9, 2014

LCM of 2, 3, 4, 5, ..., 10 = 2520

Parveen Soni
Nov 6, 2014

LCM of numbers

it's simply the LCM of the integers

yeah, you are correct

Rishi Hazra - 6 years, 7 months ago

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