LCM of 4, 7 and 10 is 140. LCM is the smallest common multiple of two or more numbers. Subject experts crafted the article LCM of Two Numbers to provide the perfect way of finding the least common multiple with ease. Using this article while solving problems helps students to have a firm grip on the LCM concept which is essential to score good marks in exams. Let us learn in detail how to calculate the least common multiple of 4, 7 and 10 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 4, 7 and 10?
The Least Common Multiple of 4, 7 and 10 is 140.
How to Find LCM of 4, 7 and 10?
LCM of 4, 7 and 10 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 4, 7 and 10 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 4, 7 and 10 can be expressed as;
4 = 2 × 2
7 = 7
10 = 2 × 5
LCM (4, 7, 10) = 2 × 2 × 5 × 7 = 140
LCM of 4, 7 and 10 Using Division Method
In the division method, to calculate the least common multiple of 4, 7 and 10, we divide the numbers 4, 7 and 10 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 4, 7 and 10.
| 2 | 4 | 7 | 10 |
| 2 | 2 | 7 | 5 |
| 5 | 1 | 7 | 5 |
| 7 | 1 | 7 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (4, 7, 10) = 2 × 2 × 5 × 7 = 140
LCM of 4, 7 and 10 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 4, 7 and 10 are as follows:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ……..,124, 128, 132, 136, 140 ……
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,………..,119, 126, 133, 140…………
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140 ………
LCM (4, 7, 10) = 140
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 4, 7, 10 exactly?
Solution: The LCM value is the smallest number that is divisible by 4, 7, 10 exactly. The LCM of 4, 7 and 10 is 140. Hence, the smallest number that is divisible by 4, 7, 10 exactly is 140.
Frequently Asked Questions on LCM of 4, 7 and 10
What is the LCM of 4, 7 and 10?
Mention the LCM of 4, 7 and 10 and the HCF of 4, 7 and 10.
140 is the LCM of 4, 7 and 10. True or False.
Name the methods used to determine the LCM of 4, 7 and 10.
The following methods are used to determine the LCM of 4, 7 and 10
Prime Factorisation
Division Method
Listing the Multiples
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