LCM of 75 and 69 is 1725. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 75 and 69, the LCM of 75 and 69 is the smallest number. 75, 150, 225, 300, 375, 450, 525, etc.) and (69, 138, 207, 276, etc.) are the first few multiples of 75 and 69, respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 75 and 69?
The answer to this question is 1725. The LCM of 75 and 69 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 75 and 69, is the smallest positive integer 1725 which is divisible by both 75 and 69 with no remainder.
How to Find LCM of 75 and 69?
LCM of 75 and 69 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 75 and 69 Using Prime Factorisation Method
The prime factorisation of 75 and 69, respectively, is given by:
75 = (3 × 5 × 5) = 31 × 52 and
69 = (3 × 23) = 31 × 23
LCM (75, 69) = 1725
LCM of 75 and 69 Using Division Method
We’ll divide the numbers (75, 69) by their prime factors to get the LCM of 75 and 69 using the division method (preferably common). The LCM of 75 and 69 is calculated by multiplying these divisors.
| 3 | 75 | 69 |
| 5 | 25 | 23 |
| 5 | 5 | 23 |
| 23 | 1 | 23 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (75, 69) = 1725
LCM of 75 and 69 Using Listing the Multiples
To calculate the LCM of 75 and 69 by listing out the common multiples, list the multiples as shown below
| Multiples of 75 | Multiples of 69 |
| 75 | 69 |
| 150 | 138 |
| 225 | 207 |
| …. | ….. |
| 1725 | 1725 |
The smallest common multiple of 75 and 69 is 1725.
Therefore LCM (75, 69) = 1725
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Video Lesson on Applications of LCM
LCM of 75 and 69 Solved Example
Question: The product of two numbers is 5175. If their GCD is 3, what is their LCM?
Solution:
Given: GCD = 3
product of numbers = 5175
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 5175/3
Therefore, the LCM is 1725.
The probable combination for the given case is LCM(75, 69) = 1725.
Frequently Asked Questions on LCM of 75 and 69
What is the LCM of 75 and 69?
List the methods used to find the LCM of 75 and 69.
If the LCM of 69 and 75 is 1725, Find its GCF.
Since the LCM of 69 and 75 = 1725
⇒ 1725 × GCF(69, 75) = 5175
Therefore, the greatest common factor = 5175/1725 = 3.
What is the Relation Between GCF and LCM of 75, 69?
What is the Least Perfect Square Divisible by 75 and 69?
LCM of 75 and 69 = 3 × 5 × 5 × 23 [Incomplete pair(s): 3, 23] ⇒ Least perfect square divisible by each 75 and 69 = LCM(75, 69) × 3 × 23 = 119025 [Square root of 119025 = √119025 = ±345] Therefore, 119025 is the required number.
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