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On this page you will found about, How to solve LCM Questions Quickly with the help of formulas and tricks. You will also get to know about the basic concepts of LCM along with different method to solve LCM Questions.
Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of the highest powers of all the factors.
Example : Find out LCM of 8 and 14
Express each number as a product of prime factors. (Reference: Prime Factorization)
8 = 2 × 2 × 2
14 = 2 × 7
LCM = The product of highest powers of all prime factors.
Here the prime factors are 2 and 7
The highest power of 2 here = 3
The highest power of 7 here = 1
Hence LCM = 2× 2× 2 × 7 = 56
Arrange the given numbers in a row in any order. Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required L.C.M. of the given numbers.
Example 2: Find out LCM of 18, 24, 9, 36 and 90
Hence Least common multiple (L.C.M) of 18, 24, 9, 36 and 90
= 2 × 2 × 2 × 3 × 3 × 5
= 360
LCM of 18, 24, 9, 36 and 90 is 360.
Question 1. What will be the least number which when doubled will be exactly divisible by 12, 14, 16, 18, and 22?
Options
A. 630
B. 5544
C. 4544
D. 2534
Solution : L.C.M. of 12, 14, 16, 18, and 22 = 11088
Required number = (11088 ÷ 2) = 5544
Correct option:B
Question 2 : The least number which when divided by 13, 17 and 19 leaves a remainder 10 in each case is?
A. 4209
B. 4290
C. 4029
D. 4902
Solution : Required number = (L.C.M of 13, 17, 19) + 10 = 4199 + 10 = 4209
Correct option:A
Question 3 : The L.C.M. of two numbers is 40. The numbers are in the ratio 2: 5. Find the sum of the number both the numbers?
A. 26
B. 25
C. 28
D. 120
Solution : Let the numbers be 2x and 5x.
Then, their L.C.M. = 10x
So, 10x = 40 or x = 4
Numbers are 2x = 2 * 4 = 8
5x = 5 * 4 = 20
Therefore, required sum = (8 + 20) = 28
Correct option:C
Question 1 : Find the LCM of 16 and 28
A. 121
B. 112
C. 211
Solution : Prime factorization of 16 = 2 * 2 * 2 * 2 = 24
Prime factorization of 28 = 2 * 2 * 7 = 22 * 71
Highest exponent value we take 24 * 71 = 112
Therefore, LCM (16, 28) = 112
Question 2 : Find the L.C.M of 0.16, 5.4 and 0. 0068
A. 734.4
B. 7344
C. 73.44
D. 7.34
Solution : L.C.M (16, 54, 68) = 7344
In numbers 0.16, 5.4, and 0.0098, the minimum digits from right to left are 5.4. Therefore, we
put decimal in our result as 734.4.
Question 3 : Find the LCM of two numbers, if the ratio of two numbers is 2: 3 and their HCF is 6.
A. 30
B. 18
C. 40
D. 36
Solution : Let the numbers be 2x and 3x
In the question, H.C.F is given as 6
Therefore, the value of x = 6
So the numbers are 2x = 2 * 6 = 12
3x = 3 * 6 = 18
L.C.M. (12, 18) = 36
Correct option:D
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