Last updated on May 26th, 2025
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 5. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
The LCM of 3 and 5 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
The LCM of 3 and 5 can be found using the following steps:
Step 1: Write down the multiples of each number
Multiples of 3 = 3,6,9,12,15 …
Multiples of 5 = 5, 10,15,20 …
Step 2:Ascertain the smallest multiple from the listed multiples
The smallest common multiple is 15.
Thus, LCM(3, 5) = 15.
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step 1:Find the prime factors of the numbers:
Prime factorization of 3 = 3
Prime factorization of 5 = 5
Take the highest powers of each prime factor:
Highest power of 3 = 3
Highest power of 5 = 5
Multiply the highest powers to get the LCM:
LCM(3, 5) = 3 × 5 = 15
This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.
Step1: Write the numbers:
Step 2 : Divide by common prime factors and multiply the divisors:
3 × 5 = 15
Thus, LCM(3, 5) = 15.
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 5, make a note while practicing.
A number n is divisible by 3 and 5. The value of n is between 20 and 40, find n.
To solve for n, we first find the LCM of the numbers 3 and 5;
Prime factorization of 3 = 31
Prime factorization of 5 = 51
LCM (3,5) = 15
15×2 = 30, a multiple of both 3 and 5.
We find a multiple of 15, that falls in the range of 20 and 40 is; 15 ×2 = 30, which is divisible by both 3 and 5.
Verify a×b = LCM (a,b) ×HCF(a,b) for 3 and 5.
a = 3, b= 5
a×b = LCM (a,b) ×HCF(a,b)
3×5 = LCM (3,5) ×HCF(3,5)
15 = 15 ×1
15 = 15
LHS = RHS in the above solution, the relationship is hence verified.
The product of a and b is 45, and the HCF is 1. a = 3, find the LCM.
We know that; a×b = LCM (a,b) ×HCF(a,b)
Given; 3×b = 45, HCF(3,b)= 1
Applying the same in the formula;
45 = LCM (3,b) ×1
LCM (3,b) = 45/1 = 45
Now we solve for b - 3×b = 45
b = 45/3 = 15
The other number is 15, LCM(3,15) = 15.
A car mechanic services a red car every 3 days and a blue car every 5 days. If the cars are serviced today, when will they be serviced next together?
The LCM of 3 and 5 is 15.
Both cars will be serviced again in 15 days, which is the smallest time interval between the digits.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.