HCF is the greatest common divisor of more than one integers. Hence, the largest positive integer that divides more than one integers known as Highest common factor. LCM is the least common multiple of two or more integers. Let us move forward and look up for some of the Tips and Tricks Of HCF and LCM.
Question 1. Find the greatest 5 digit number divisible by 5, 15, 20, and 25
Options
A. 99900
B. 99000
C. 99990
D. 90990
Solution :
LCM of 5, 15, 20, and 25 is 300
The greatest 5 digit number is 99999
$\frac{99999}{300} = 99$
Therefore, required number 99999 – 99 = 99900
Correct option: A
Their ratio and H.C.F. are given.
Product of H.C.F. and L.C.M are given
Question 2. The product of two numbers is 3888. If the H.C.F. of these numbers is 36, then the greater number is:
Options
A. 110
B. 108
C. 36
D. 120
Solution :
Let the two numbers be 36x and 36y
Now, 36x * 36y = 3888
$xy =\frac{3888}{36 × 36}$
xy = 3
Now, co-primes with product 3 are (1, 3).
Therefore, the required numbers are 36 * 1 = 36
36 * 3 = 108
Therefore the greatest number is 108
Correct option: B
Question: Sum of two numbers is 60 and the H.C.F. and L.C.M. of these numbers are 5 and 100 respectively, then the sum of the reciprocals of the numbers is equals to:
Options
A. $\frac{3}{25}$
B. $\frac{11}{220}$
C. $\frac{21}{120}$
D. $\frac{11}{320}$
Solution :
Let the numbers be a and b.
Now , given a+b = 60
a × b = HCF × LCM = 5 × 100
= 500
$\frac{1}{a} +\frac{1}{b} = \frac{a+b}{a × b}$
$\frac{1}{a} +\frac{1}{b} = \frac{60}{500}$
$\frac{3}{25}$
Correct option: A
Question : Suppose there are three different containers contain different quantities of a mixture of Sugar and rice whose measurements are 403 grams, 434 grams and 465 grams What biggest measure must be there to measure all the different quantities exactly?
Options
A. 31 grams
B. 21 grams
C. 41 grams
D. 30 litres
Solution :
Prime factorization of 403, 434 and 465 is
403=13×31
434=2×7×31
465=3×5×31
H.C.F of 403, 434 and 465=31
Correct option: A
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
Options
A. 8
B. 16
C. 9
D. 10
Solution :
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
Hence, the bells will toll together after every 120 seconds(2 minutes).
Therefore, in 30 minutes ,number of times bells toll together is $\frac{30}{2} + 1 = 16$
Correct option: B
Question: Two people P and Q start running towards a circular track of length 400 m in opposite directions with initial speeds of 10 m/s and 40 m/s respectively. Whenever they meet, P’s speed doubles and Q’s speed halves. After what time from the start will they meet for the third time?
Options
A. 30 seconds
B. 26 seconds
C. 10 seconds
D. 20 seconds
Solution :
Time taken to meet for the 1st time= $\frac{400}{40+10}$ = 8 sec.
Now P’s speed = 20m/s and Q’s speed=20 m/s.
Time taken to meet for the 2nd time = $\frac{400}{20+20}$ = 10 sec.
Now P’s speed = 40 m/sec and Q’s speed = 10 m/sec.
Time taken to meet for the 3rd time= $\frac{400}{10+40}$ = 8 sec.
Therefore, Total time= (8+10+8) = 26 seconds.
Correct option: B
Question. 3 Find HCF of 12 and 16.
Options
A. 5
B. 4
C. 12
D. 16
Solution :
Find the difference between 12 and 16. The difference is 4. Now, check whether the numbers are divisible by the difference. 12 is divisible by 4 and 16 is divisible by 4.Hence, the HCF is 4.
Correct option: B
Question. 4 Find HCF of 18 and 22.
Options
A. 2
B. 4
C. 18
D. 36
Solution :
Find the difference between 18 and 22. The difference is 4. Now, check whether the numbers are divisible by the difference. Both 18 and 22 are not divisible by 4. So take the factors of the difference. The factors of 4 are 2*2*1. Now, check whether the numbers are divisible by the factors. 18 and 22 are divisible by factor 2.
Hence, the HCF is 2.
Note: If there are more than two numbers, take the least difference.
Correct option: A
Question 5 Find LCM of 2,4,8,16.
Options
A. 16
B. 18
C. 12
D. 2
Solution :
Factorize of above numbe
$2 = 2 $
$8 = 2^3$
$16 = 2^4$
Choose the largest number. In this example, the largest number is 16. Check whether 16 is divisible by all other remaining numbers. 16 is divisible by 2, 4, 8. Hence, the LCM is 16.
Correct option: A