• 072920 77839
  • info@smartachievers.in
Menu
Back
  • JEE ADVANCE
  • JEE MAIN
  • NEET
  • BITSAT
  • CBSE BOARD
  • UP BOARD
  • CUET
JEE ADVANCE
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
JEE MAIN
  • CLASS XI - XII
  • CRASH COURSE
CRASH COURSE
NEET
  • CLASS XI - XII
  • CRASH COURSE
BITSAT
  • CLASS XI - XII
CBSE BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
  • CLASS VI
  • CLASS VII
  • CLASS VIII
UP BOARD
  • CLASS IX
  • CLASS X
  • CLASS XI
  • CLASS XII
CUET
  • CRASH COURSE
Courses


Solution


Q.

What is the least number that is divisible by all the numbers from 1 to 10
1 420  
2 840  
3 2520  
4 3200  

Ans.

(3)  

For any number to be divisible by all the numbers from 1 to 10, we need LCM of the numbers from 1 to 10. So, it must have maximum powers of each prime number that can be obtained in prime factorisation of numbers from 1 to 10.

∴ 1 = 12 = 2¹3 = 3¹4 = 2²5 = 5¹6 = 2¹ × 3¹7 = 7¹8 = 2³9 = 3²10 = 2¹ × 5¹So, required least number = 2³ × 3² × 5¹ × 7¹ = 8 × 9 × 5 × 7 = 2520