HCF & LCM Practice Set

Q1. 12²,12⁴,12¹⁰,12⁶ Find the L.C.M.

1. a) 12 b) 12²c)12⁶ d)12¹⁰

Q2. 6^-1,6^-3,6^-10,6^-12 Find the H.C.F.
 a) 6^-1 b) 1 c)6^-12 d)6^-11

Q3. The L.C.M of the fraction of ²/3,⁴/9,⁵/6,⁷/12 is:

a)³⁵/9 b)¹/36 c) ¹/18 d)¹⁴⁰/3

 Q4.The ratio of two number is 5:6, if their H,C.F. is 9 and L.C.M. is 270. Find the numbers.
a) 72,63 b) 81,108 c) 45,54 d) 225,108

Q5. The multiplication of two numbers is 20,000 if their L.C.M is 800. Find the H.C.F.
a)400 b) 25 c) 2,000 d) 800

Q6. Find the least number which when divided by 4,6,7,8,9,12. leaves the same remainder 3 in each case.
a) 504 b) 501 c) 507 d) 506

Q7. The smallest number which is divisible by 12,15,20 and is a perfect square is:
a) 400 b) 900 c) 1600 d) 3600

Q8. The largest number which divided by 77, 147 and 252 to leave the same remainder in each case is:
a) 9 b) 15 c)35 d) 25

Q9. The H.C.F. of the fraction of ³⁶/25,⁴⁸/25,⁷²/75
a)¹²/75 b) ⁴/25 c) ³⁶/25 d) ³⁶

Solution:

(1)
Sol: Option (d)

 12²,12⁴,12¹⁰,12⁶ Find the L.C.M.
L.C.M. = 12¹⁰ 

(2)
Sol: Option(c)

6^-1,6^-3,6^-10,6^-12 Find the H.C.F.

¹/₆,¹/₆³ ,¹/₆¹⁰ ,¹/₆¹² 

H.C.F.= ^H.C.F./_L.C.M.= ¹/₆¹² 
= 16^-12

(3)
Sol: Option (d)

Fraction of L.C.M. = ^L.C.M./H.C.F. =¹⁴⁰/3

(4)
Sol: Option (c)
The ratio of numbers is 5:6
The number is 5✘9=45
=6✘9=54

(5)
Sol: Option (b)
L.C.M.✘H.C.F. = Ist No✘2nd No.
800✘H.C.F. = 20,000
H.C.F. = ^20,000/₈₀₀ = 25

(6)
Sol: Option (c)
L.C.M. of the number 4,6,7,8,9,12
L.C.M. = 8✘9✘7 = 504
and Remainder = 3
So the number is L.C.M. + 3
 504 + 3 = 507

(7)
Sol: Option (b)
L.C.M. = (3✘5✘2²)
Required number = ( 3²✘5²✘2²)=900

(8)
Sol: Option (c)
Required number = H.C.F. of (147-77)
(252-147) and (252-77)
= H.C.F. of 70,105 and 175
= 35
( 70 = 2✘5✘7, 105 = 5✘3✘7 and 175=5✘5✘7 )
H.C.F. =5✘7 = 35

(9)
Sol: Option (a)
= ^{H.C.F. of numerator}/ L.C.M. of denominator
H.C.F.= ¹²/75