## H.C.F and L.C.M Questions - 1

Find the HCF of 84, 280 and 364
• 84
• 36
• 28
• 42
• 21
Explanation

HCF is the highest common factor which divides all the given numbers exactly.

 280 ) 364 ( 1 280 84 ) 280 ( 3 252 28 ) 84 ( 3 84 0

As last divisor is 28, then HCF is 28.

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Three different containers contain 144 liters, 192 liters and 288 liters of petrol respectively. Which biggest measure can measure all these different quantities exactly ?
• 46 liters
• 72 liters
• 96 liters
• 63 liters
• 64 liters
Explanation

HCF of 144, 192 and 288 is

 192 ) 288 ( 1 Â Â Â Â Â Â Â Â Â 192 Â Â Â Â Â Â Â Â Â Â Â 96 ) 192 ( 2 Â Â Â Â Â Â Â Â Â 192 Â Â Â Â Â Â Â Â Â Â Â 0 Â Â Â Â Â Â Â

0 =>Â  HCF of 192 and 288 is 96, again HCF of 144 and 192 is

 144 ) 192 ( 1 Â Â Â Â Â Â Â Â Â 144 Â Â Â Â Â Â Â Â Â Â Â 48 ) 144 ( 3 Â Â Â Â Â Â Â Â Â 144 Â Â Â Â Â Â Â Â Â Â Â 0 Â Â Â Â Â Â Â

HCF of 144, 192 and 288 is 46, 46 liter is the biggest measure, that can be used.

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Three numbers are in the ratio 2:3:5 respectively, and their HCF is 15. What are the numbers ?
• 45, 75, 30
• 30, 45, 75
• 30, 75, 45
• 15, 30, 45
• 45, 60, 90
Explanation

Let the numbers be 2a: 3a: 5a, then HCF of the numbers would be â€˜aâ€™

Therefore the numbers are 2 x 15 = 30, 3 x 15 = 45, 5 x 15 = 75

Workspace
What is the largest number that will divide 109, 206 and 303 leaving the same remainder in each case ?
• 32
• 81
• 63
• 97
• 67
Explanation

Greatest number that can divide x, y and z, leaving the same remainder in each case is

HCF of ( x â€“ y ), ( y â€“ z ) ( z â€“ x ) [ i.e. the difference between the given numbers]

( 303 â€“ 206) = 97, ( 303 â€“ 109 ) = 194, (206 â€“ 109 ) = 97.

HCF of 97 is 97 and 194 is 97 = > Hence answer is 97

Workspace
What is the largest size of tile that can be paved in a room measuring 18 feet breadth and 24 feet length ?
• 12 feet
• 4 feet
• 9 feet
• 3 feet
• 6 feet
Explanation

HCF of 24 and 18 is 6 or 6 feet

Therefore answer is 6 feet.

Workspace
The sum of two numbers is 252 and their HCF is 36. What are the numbers ?
• 78, 174
• 92, 160
• 66, 186
• 108, 144
• 87, 165
Explanation

Let the number be 36a + 36b

$$Then \ a \ + \ b \ = \ \frac{252}{36} \ = \ 7$$

Co â€“ Primes which sums up 7 are => (1,6) (2,5) (3,4)

The numbers can be (36, 216) or (72, 180) or (108, 144)

Out of these we have 108, 144 in the choices.

Workspace
Find LCM of 12, 18 and 26
• 336
• 468
• 624
• 182
• 268
Explanation

LCM of 12, 18 and 26 is

$$\begin{array}{c|lcr} 2 & \text{12} & \text{18} & \text{26} \\ \hline 2 & \text{6} & \text{9} & \text{13} \\ \hline 3 & \text{3} & \text{9} & \text{13} \\ \hline & \text{1} & \text{3} & \text{13} \\ \end{array}$$

= > 22 x 32 x 13 or 4 x 9 x 13 = 468

Workspace
What is the least number which when divided by 24, 32 and 48, leaves 7 as its remainder ?
• 55
• 39
• 113
• 65
• 105
Explanation

LCM of 24, 32 and 48 is 96.

Required number = 96 + 7 = 113.

Workspace
What is the largest four digit number which is divisible by each one of 12, 14, 15 and 18 ?
• 9620
• 9720
• 9820
• 8820
• 8920
Explanation

LCM of 12, 14, 15 and 18 is 1260.

Largest 4 digit number divisible by 1260 is 8820 { Multiple of 1260 }

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What is the least number which when divided by 16, 18, 22 and 27 leaves the remainders 8, 10, 14 and 19 respectively ?
• 4760
• 4744
• 4752
• 4764
• 4780
Explanation

( 16 â€“ 8 ) = 8, ( 18 â€“ 10 ) = 8, ( 22 â€“ 14 ) = 8, (27 â€“ 19 ) = 8

LCM of 16, 18, 22 and 27 is 4752

Required number is 4752 â€“ 8 = 4744

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## Quantitative Aptitude H.C.F and L.C.M Important Formulas

Highest Common Factor / Greatest Common Measure [H.C.F/G.C.M]: The H.C.F. of two or more than two numbers is the greatest number that divides each one of them exactly.

## H.C.F by Factorization:

Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives HCF.

## H.C.F. by Division Method:

• To find the HCF of two given numbers divide the larger number by the smallest.
• Divide the divisor by the remainder. Repeat the process of dividing by the preceding divisor by the remainder last obtained till Zero is obtained as remainder.
• The last divisor is the required HCF.

## Lowest Common Multiple [L.C.M]

The least number which is exactly divisible by each one of the given numbers is called their LCM.

## LCM by Factorization Method:

Express each one of the given numbers as the product of prime factors. The product of highest powers of all prime factors gives LCM.

• Product of two numbers =Â  Product of their HCF & LCM

## H.C.F & L.C.M of Fractions:

HCF = $\displaystyle \frac{\text{HCF of Numerators}}{\text {LCM of Denominators}}$

LCM = $\displaystyle \frac{\text{LCM of Numerators}}{\text{HCF of Denominators}}$

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