LCM of 75 and 105 is 525. LCM can be defined as the smallest common multiple of two or more numbers. The article Least Common Multiple (LCM) is formulated by subject matter experts to help students speed up their problem-solving skills based on the LCM. The faculty explain the LCM concept in simple language so that students can learn it without further confusion. In this article, let us learn how to find the least common multiple of 75 and 105 in a precise manner.
What is LCM of 75 and 105?
The Least Common Multiple of 75 and 105 is 525.
How to Find LCM of 75 and 105?
LCM of 75 and 105 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 75 and 105 Using Prime Factorisation Method
In the prime factorisation method, 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.
75 = 3 × 5 × 5
105 = 3 × 5 × 7
LCM (75, 105) = 3 × 5 × 5 × 7 = 525
LCM of 75 and 105 Using Division Method
In the division method, to determine the least common multiple of 75 and 105, we divide the numbers 75 and 105 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 75 and 105.
| 3 | 75 | 105 |
| 5 | 25 | 35 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (75, 105) = 3 × 5 × 5 × 7 = 525
LCM of 75 and 105 Using Listing the Multiples
In this method, we list the multiples of 75 and 105 to find the least common multiple among them. Let us glance at the multiples of 75 and 105 from the table given below.
| Multiples of 75 | Multiples of 105 |
| 75 | 105 |
| 150 | 210 |
| 225 | 315 |
| 300 | 420 |
| 375 | 525 |
| 450 | 630 |
| 525 | 735 |
| 600 | 840 |
LCM (75, 105) = 525
Related Articles
- LCM of Two Numbers
- LCM Calculator
- Prime Factorization and Division Method for LCM and HCF
- LCM Formula
- LCM with Examples
- HCF and LCM
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 75 and 105?
Solution: 525 is the smallest number that is divisible by both 75 and 105.
2. The GCD and LCM of the two numbers are 15 and 525. If one number is 75, what is the other number?
Solution: Let the other number be k
We know that
GCD × LCM = 75 × k
k = (GCD × LCM) / 75
k = (15 × 525) / 75
k = 105
Therefore the other number is 105.
Frequently Asked Questions on LCM of 75 and 105
What is the LCM of 75 and 105?
Is the LCM of 75 and 105 the same as the HCF of 75 and 105?
Name the methods used to find the least common multiple of 75 and 105.
The methods used to find the least common multiple of 75 and 105 are:
Prime Factorisation
Division method
Listing the Multiples
Calculate the GCF if the LCM of 75 and 105 is 525.
GCF × LCM = 75 × 105
Given
LCM = 525
GCF × 525 = 75 × 105
GCF = 15
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