LCM of 7 and 17 is 119. The LCM is the method to find the least common multiple between any two or more numbers. Prime Factorisation and Division Method for LCM and HCF are formulated by experts with suitable examples to explain the LCM and HCF concept in the most understandable language. Students can use this article to learn how tricky problems are solved, which in turn helps them build their time management and problem-solving skills. Let us learn in detail how to verify the least common multiple of 7 and 17 in this article.
What is LCM of 7 and 17?
The Least Common Multiple of 7 and 17 is 119.
How to Find LCM of 7 and 17?
LCM of 7 and 17 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 7 and 17 Using Prime Factorisation Method
In the prime factorisation method, LCM of 7 and 17 can be obtained by multiplying prime factors raised to their respective highest power.
7 = 7
17 = 17
LCM (7, 17) = 7 × 17 = 119
LCM of 7 and 17 Using Division Method
In the division method, to find the least common multiple of 7 and 17, we divide the numbers 7 and 17 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 7 and 17.
| 7 | 7 | 17 |
| 17 | 1 | 17 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (7, 17) = 7 × 17 = 119
LCM of 7 and 17 Using Listing the Multiples
In this method, we list down the multiples of 7 and 17 to find the least common multiple among them. The multiples of 7 and 17 are provided below
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ………., 105, 112, 119, …………
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, …………
LCM (7, 17) = 119
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Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 7 and 17?
Solution: 119 is the smallest number that is divisible by both 7 and 17.
2. The GCD and LCM of the two numbers are 1 and 119. If one number is 17, what is the other number?
Solution: Let the other number be k
We know that,
GCD × LCM = 17 × k
k = (GCD × LCM) / 17
k = (1 × 119) / 17
k = 7
Hence the other number is 7.
Frequently Asked Questions on LCM of 7 and 17
What is the LCM of 7 and 17?
Mention the LCM of 7 and 17 and the HCF of 7 and 17.
Name the methods used to find the LCM of 7 and 17.
The methods used to find the LCM of 7 and 17 are as follows:
Prime Factorisation
Division method
Listing the Multiples
Find the GCF if the LCM of 7 and 17 is 119.
GCF × LCM = 7 × 17
Given
LCM = 119
GCF × 119 = 7 × 17
GCF = 1
Write the relation between GCF and LCM of 7 and 17.
The relation between GCF and LCM of 7 and 17 is
GCF × LCM = 7 × 17
GCF × LCM = 119
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