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173 LearnersLast updated on November 30th, 2024
LCM of 10 and 15
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 15. 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 10 and 15?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 10 and 15 using the Listing Multiples Method
The LCM of 10 and 15 can be found ascertained using the following steps
Steps:
- Write down the multiples of each number
- Multiples of 10 = 10, 20, 30, 40,60 …
- Multiples of 15 = 15,30,45,60,75,…
- Ascertain the smallest multiple from the listed multiples
- The smallest common multiple is 30. Thus, LCM(10,15) = 30.
LCM of 10 and 15 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.
Steps:
- Find the prime factors of each number:
- Prime factorization of 10 =2×5
- Prime factorization of 15 =5×3
- Take the highest powers of each prime factor and multiply the highest powers to get the LCM:
- LCM(10,15) = 2×3×5= 30
LCM of 10 and 15 using the Division Method
This method involves dividing both numbers by their common prime factors until no further division is possible, and then multiplying the divisors to find the LCM.
Steps:
- Write the numbers:
- Divide by common prime factors
Multiply the divisors: So, LCM(10,15) = 30
Common Mistakes and how to avoid them while finding the LCM of 10 and 15
LCM of 10 and 15 Examples
Problem 1
Buses A and B run every 10 days and 15 days respectively. In how many days will they run together again?
Explanation
Problem 2
A company has meetings every 10 days and 15 days. If both the conference rooms are booked today, when will they next be booked together ?
Explanation
Problem 3
Warehouse XYZ restocks sugar every 10 days and pulses every 15 days. If both the goods are restocked today, when will they next be restocked?
Explanation
Problem 4
The sprinkler watering system waters every 10 days and the drip watering system waters every 15 days. On which day do they have to be turned on together?
Explanation
FAQs on LCM of 10 and 15
1.Why is the LCM of 10 and 15 not simply their product (10 × 15 = 150) ?
2.What is the LCM formula using the HCF ?
3.What is the LCM of 10,15 and 30?
4.What is the LCM of 10,15,25?
5.What is the LCM of 5,10,15,20?
Important glossaries on the LCM of 10 and 15
- Multiple: A number multiplied with an integer.
- Prime Factor: A natural number (other than 1) whose factors that are one and itself.
- Prime Factorization: Breaking down a number into its prime factors is called Prime Factorization.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
