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116 LearnersLast updated on September 26th, 2024
LCM of 15,20 and 25
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 15,20 and 25. 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.
What is the LCM of 15,20 and 25?
The LCM of 15,20 and 25 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.
How to find the LCM of 15,20 and 25?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 15,20 and 25 using the Listing Multiples Method
The LCM of 15,20 and 25 can be found using the following steps:
Step1: Write down the multiples of each number
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180…300
Multiples of 20= 20,40,60,80,100,120,140,160,180,…300
Multiples of 25 = 25,50,75,100,125,150,175,200…300
Step2: Ascertain the smallest multiple from the listed multiples
The smallest common multiple is 300
Thus, LCM (15,20,25) = 300
LCM of 15,20 and 25 using the Prime Factorization Method
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 15 = 5×3
Prime factorization of 20 = 5×2×2
Prime factorization of 25 = 5×5
Step2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:
5×3×2×2×5 = 300
LCM (15,20,25) = 300
LCM of 15,20 and 25 using the Division Method
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.
Step 1: Write the numbers, divide by common prime factors and multiply the divisors.
Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.bring down the numbers not divisible by the previously chosen prime number.
Step 3:Continue dividing the numbers until the last row of the results is ‘1’ .
2×2×3×5×5 = 300
Thus, LCM (15,20,25) = 300
Important glossaries for the LCM of 15,20 and 25
Multiple: A number and any integer multiplied.
Prime Factor: A natural number (other than 1) that has factors that are one and itself.
Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.