Last updated on May 26th, 2025
LCM is the smallest number divisible by 3, 5 and 10. LCM helps to solve problems with fractions, and scenarios like managing supplies and restocking. In this article, we will learn how to find LCM of 3, 5 and 10 by using different methods.
The LCM of 3, 5 and 10 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. The methods to find the LCM are:
In the listing method, we write a multiple of the numbers first and then find the smallest common multiple.
Step 1: Identify the multiples of 3, 5 and 10
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50….
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90….
Step 2: Ascertain the smallest multiple from the listed multiples of 3, 5 and 10
The LCM of 3, 5 and 10 is 30
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 3, 5 and 10
Prime factorization of 3: 31
Prime factorization of 5: 51
Prime factorization of 10: 21 × 51
Step 2: Multiply the highest power of each factor ascertained to get the LCM
LCM of 3, 5 and 10 = 21 × 31 × 51 = 30
This method involves simultaneously dividing the numbers by their prime factors until they become 1 and multiplying the divisors to get the LCM.
Step 1: Write the numbers in a row, like 3, 5, 10.
Step 2: Start dividing the numbers with prime factors by 2
From the numbers 3, 5 and 10, only 10 is divisible by 2 (10 ÷
2) which gives 5 as the quotient.
Now the numbers in the row will be 3, 5, 5
Step 3: Move on to the next prime number, 3
From the list 3, 5 and 5, only 3 is divisible by 3 (3 ÷ 3) which gives 1 as the quotient.
Now the numbers in the row will look like 1, 5, 5.
Step 4: Move on to the next prime number 5.
From the list 1, 5 and 5, only 5 is divisible by 5 (5 ÷ 5) which gives 1 as the quotient.
Now the numbers in the row will look like 1, 1, 1.
Step 5: To find the LCM, multiply all the divisors used
The divisors used are 2, 3 and 5. The product of 2, 3 and 5 is 30 (2×3×5 = 30)
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3, 5 and 10 make a note while practicing.
Can you tell whether the LCM of 3, 5 and 10 is 30? Also find the GCF of 3, 5 and 10
Yes, the LCM is 30. The GCF of 3, 5 and 10 is 1.
We can find the LCM of 30 by listing the multiples of 3, 5 and 10, and finding the least common multiple.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33….
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50….
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90…
The LCM is 30
To find the GCF, list the factors of 3, 5 and 10, and find the GCF. Factors of 3 are 1 and 3, factors of 5 are 1 and 5,
the factors of 10 are 1, 2 and 5. So the GCF is 1.
Runner A runs every 3 minutes in a trail and runner B every 5 minutes and runner C runs every 10 minutes, and both of them start together. When will they both meet at the starting point again?
The LCM of 3, 5 and 10 is 30.
Runner A and B will meet at the starting point in 30 minutes, the LCM of 3, 5 and 10 is 30, which is the smallest common time interval for the given digits.
What will be the product when the LCM of 3,5 and 10 is multiplied twice?
The product will be 900
The LCM is 30. When 30 is multiplied twice, we get 900 as the product (30 × 30 = 900)
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.