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MATHS SOLVED IN STEPS: HCM & LCM - 02

PSC WINNERS 10:59 AM
16. Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?
    A. 28      B. 40        C. 64        D. 42
Answer : Option B
    Explanation :
     Let the numbers be 2x and 3x
     LCM of 2x and 3x = 6x (? LCM of 2 and 3 is 6. Hence LCM of 2x and 3x is 6x)
Given that  LCM of 2x and 3x is 48
 => 6x = 48
 => x =48#6=8
Sum of the numbers = 2x + 3x = 5x = 5 × 8 = 40

17. What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?
A. 9800         B. 9600         C. 9400        D. 9200
Answer : Option B
Explanation :
Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600

18.   Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
A. 40         B. 30            C. 20          D. 10
Answer : Option C
Explanation :
Let the numbers be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
=> 12x = 240
=> x = 240÷12=20
H.C.F of 2x, 3x and 4x = x = 20

19. What is the lowest common multiple of 12, 36 and 20?
A. 160             B. 220           C. 120          D. 180
Answer : Option D
Explanation :
LCM OF 12,36,20= 180

20. What is the least number which when divided by 5, 6, 7 and 8 leaves a
remainder 3, but when divided by 9 leaves no remainder?
A. 1108              B. 1683              C. 2007          D. 336
Answer : Option B
Explanation :
LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9
If k = 1, number = (840 × 1) + 3 = 843
which is not divisible by 9
If k = 2, number = (840 × 2) + 3 = 1683
which is divisible by 9
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a
remainder 3, but when divided by 9 leaves no remainder

21. The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is25, then the other is:
A. 30           B. 28              C. 24          D. 20
Answer : Option A
Explanation :
Product of two numbers = Product of their HCF and LCM.
Let one number = x
 25×x =5×150
 x=  (5×150)÷25
X=30

22. 504 can be expressed as a product of primes as
A. 2 × 2 × 3 × 3 × 7 × 7
B. 2 × 3 × 3 × 3 × 7 × 7
C. 2 × 3 × 3 × 3 × 3 × 7
D. 2 × 2 × 2 × 3 × 3 × 7
Answer : Option D
Explanation :
It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7
* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> Problems on Average
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Age 
* MATHS (SOLVED IN STEPS ==> Pipe and Cisterns
* MATHS (SOLVED IN STEPS ==> ODD MAN
* MATHS (SOLVED IN STEPS ==> TIME & WORK

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