**Questions:**

Practice Questions on HCF and LCM for CLAT

- Find the HCF of 2923 and 3239.
- Find the LCM of 2
^{3}* 3^{2 }* 5^{2}*7 ; 2^{5 }* 5^{3 }* 7^{2 }; 2^{2 }* 3^{3}* 5^{3 }* 11 and 3^{4}* 7 * 11^{3} - The ratio of two numbers is 3:5, their HCF is 12. Find the numbers.
- If the product of two co-prime numbers is 117, then find their LCM.
- The product of the LCM and HCF of two numbers is 48. Difference between the two numbers is 4. Find the greater number among them.
- LCM and HCF of two numbers are 13 and 455 respectively. If one of the numbers lie between 75 and 125, then find that number.
- Six bells start toll together and tolls at regular intervals of 2,4,6,8,10 and 12 respectively. In 30 minutes how many times they would have tolled together.
- Find the least number which when increased by 3 is divisible by each one 24, 32, 36 and 54
- Find the greatest possible length which can be used to measure lengths 7m, 3m 85cm and 12m 95cm.
- If N is the greatest number dividing 1305, 4665 and 6905 leaving the same remainder in each case, then Find the sum of digits of N.

**Solutions:**

*Ans: 79*

**2923 ) 3239 ( 1**

** 2923**

** 316 ) 2923 ( 9**

** 2844**

** 79 ) 316 ( 4**

** 316**

** 00**

*Ans: 2*^{5}* 3^{3}* 5^{3}* 7^{2}* 11^{3}

Select the prime numbers with the highest powers and multiply them.

*Ans: 36 & 60*

Given: Two numbers ratio= 3:4 i.e., numbers => 3x and 4x

HCF = 12; as x is the highest common factor in the above numbers therefore x=12

Numbers => 3*12 =36 & 5*12 = 60

*A**ns: 117*

Concept of Co – prime and HCF i.e., HCF of two co-prime numbers is 1

LCM * HCF = Product of two numbers

LCM * 1 = 117 ; LCM = 117

*Ans: 6*

Let two numbers be a and b

Therefore, a*b = 48 ; a-b = 8

Solving above equations we get, a=12 and b=4

*Ans: 91*

Given: LCM = 455 ; HCF=13

Product of numbers = LCM * HCF

=13*455 = 5915

Let the numbers be 13a and 13b ; 13a*13b = 5915

a*b = 35

Co-prime with product 35 are (1,35) and (5,7)

So, the numbers can be (1*13, 35*13) and (5*13, 7*13)

But one of the numbers lie between 75 and 125 that would be 91 giving us a suitable pair i.e., (65,91)

*Ans: 16*

LCM of 2,4,6,8,10 and 12 is 120

Bells toll together after every 120 seconds i.e., 2 minutes

In 30 minutes they will toll together for (30/2 + 1) times i.e., 16 times

*Ans: 867*

LCM (24,32,36,54) = 864

As the question demands divisibility after increment therefore answer would be LCM+3 i.e., 864+3 = 867

**Ans: 35cm**

Given: Lengths = 700cm; 385cm ; 1295cm

HCF = 35cm (greatest possible length for measure = HCF)

*Ans: 4*

N= HCF of (4665-1305), (6905-1305) and (6905-4665)

HCF of 3360, 2240 and 5600

N= 1120

Sum of Digits of N= 1+1+2+0 = 4