LCM of 90 and 140 is 1260. LCM can be defined as the smallest common multiple of two or more numbers. The highly experienced subject matter experts designed the article LCM of Two Numbers in simple and easy language to help students understand the LCM concept effortlessly. Following this article, students will be able to know the right way to approach the problems which would appear in the board exams. In this article, let us learn the simple method to find the least common multiple of 90 and 140.
What is LCM of 90 and 140?
The Least Common Multiple of 90 and 140 is 1260.
How to Find LCM of 90 and 140?
LCM of 90 and 140 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 90 and 140 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.
90 = 2 × 3 × 3 × 5
140 = 2 × 2 × 5 × 7
LCM (90, 140) = 2 × 2 × 3 × 3 × 5 × 7 = 1260
LCM of 90 and 140 Using Division Method
In the division method, to determine the least common multiple of 90 and 140, we divide the numbers 90 and 140 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 90 and 140.
| 2 | 90 | 140 |
| 2 | 45 | 70 |
| 3 | 45 | 35 |
| 3 | 15 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (90, 140) = 2 × 2 × 3 × 3 × 5 × 7 = 1260
LCM of 90 and 140 Using Listing the Multiples
In this method, we list the multiples of 90 and 140 to find the least common multiple among them. Let us glance at the multiples of 90 and 140 provided below.
Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, 1170, 1260……….
Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, …………..
LCM (90, 140) = 1260
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Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 90 and 140?
Solution: 1260 is the smallest number that is divisible by both 90 and 140.
2. The GCD and LCM of the two numbers are 10 and 1260. If one number is 90, calculate the other number.
Solution: Let the other number be k
We know that,
GCD × LCM = 90 × k
k = (GCD × LCM) / 90
k = (10 × 1260) / 90
k = 140
Hence the other number is 140.
Frequently Asked Questions on LCM of 90 and 140
What is the LCM of 90 and 140?
Is the LCM of 90 and 140 the same as the HCF of 90 and 140?
Name the methods used to find the least common multiple of 90 and 140.
The methods used to find the least common multiple of 90 140 are:
Prime Factorisation
Division method
Listing the Multiples
Determine the GCF if the LCM of 90 and 140 is 1260.
GCF × LCM = 90 × 140
Given
LCM = 1260
GCF × 1260 = 90 × 140
GCF = 10
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