Last updated on May 26th, 2025
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 25. LCM helps to solve problems with fractions and scenarios like setting an alarm or planning to align events.
The LCM of 10 and 25 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction 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;
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step 1 :Write down the multiples of each number:
Multiples of 10 = 10,20,30,40,50,…
Multiples of 25 = 25,50,75,…
Step 2: Ascertain the smallest multiple from the listed multiples of 10 and 25.
The LCM (Least common multiple) of 10 and 25 is 50. i.e., 50 is divisible by 10 and 25 with no reminder.
This method involves finding the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 10 = 2×5
Prime factorization of 25 = 5×5
Take the highest power of each prime factor and multiply the ascertained factors to get the LCM:
LCM (10,25) = 50
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1: Write down the numbers in a row;
Step 2: Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.
Step 3: Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
Step 3: The LCM of the numbers is the product of the prime numbers in the first column, i.e.,
LCM (10,25) = 50
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 25, make a note while practicing.
The LCM of a and b is 50. Given a is 10, find b.
Using the formula;
LCM(a,b) =a×b/HCF(a,b)
a =10, b= ?
LCM (a, b) = 50
The factors of 10 (a) are — 1,2,5,10; so we can assume that the HCF is one of these numbers.
By testing the values, we find the possible values of b.
Testing for 10;
25 = 10×b/10
b = 25
Testing for 5;
25 = 10×b/5
b = 12.5
Testing for 2;
25 = 10×b/2
b = 5
Testing for 1;
25 =10×b/1
b = 2.5 → cannot be true, 2.5 is not a whole number
b is possibly one of 5 and 25.
If a number is 40% of the LCM of 10 and 25, find the number.
LCM of 10,25 = 50
40% of 50 → 40/100×50 = 20
40% of the LCM is 20.
Trains A and B arrive every 10 minutes and 25 minutes at the station at the same time. In how long will they arrive together again?
The LCM of 10 and 25 = 50
The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 25 minutes.
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.