LCM of 20 and 70 is 140. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 20 and 70 is the smallest number among all common multiples of 20 and 70. The first few multiples of 20 and 70 are (20, 40, 60, 80, 100, 120, . . . ) and (70, 140, 210, 280, 350, . . . ) 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 20 and 70?
The answer to this question is 140. The LCM of 20 and 70 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 20 and 70, is the smallest positive integer 140 which is divisible by both 20 and 70 with no remainder.
How to Find LCM of 20 and 70?
LCM of 20 and 70 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20 and 70 Using Prime Factorisation Method
The prime factorisation of 20 and 70, respectively, is given by:
20 = (2 × 2 × 5) = 22 × 51 and
70 = (2 × 5 × 7) = 21 × 51 × 71
LCM (20, 70) = 140
LCM of 20 and 70 Using Division Method
We’ll divide the numbers (20, 70) by their prime factors to get the LCM of 20 and 70 using the division method (preferably common). The LCM of 20 and 70 is calculated by multiplying these divisors.
| 2 | 20 | 70 |
| 2 | 10 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (20, 70) = 140
LCM of 20 and 70 Using Listing the Multiples
To calculate the LCM of 20 and 70 by listing out the common multiples, list the multiples as shown below
| Multiples of 20 | Multiples of 70 |
| 20 | 70 |
| 40 | 140 |
| 60 | 210 |
| 80 | 280 |
| 100 | 350 |
| 120 | 420 |
| 140 | 490 |
The smallest common multiple of 20 and 70 is 140.
Therefore LCM (20, 70) = 140
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Video Lesson on Applications of LCM
LCM of 20 and 70 Solved Example
Verify the relationship between GCF and LCM of 20 and 70.
Solution:
The relation between GCF and LCM of 20 and 70 is given as,
LCM(20, 70) × GCF(20, 70) = Product of 20, 70
Prime factorization of 20 and 70 is given as, 20 = (2 × 2 × 5) = 22 × 5 and 70 = (2 × 5 × 7) = 2 × 5 × 7
LCM(20, 70) = 140
GCF(20, 70) = 10
LHS = LCM(20, 70) × GCF(20, 70) = 140 × 10 = 1400
RHS = Product of 20, 70 = 20 × 70 = 1400
⇒ LHS = RHS = 1400
Hence, verified.
Frequently Asked Questions on LCM of 20 and 70
What is the LCM of 20 and 70?
List the methods used to find the LCM of 20 and 70.
What is the Least Perfect Square Divisible by 20 and 70?
LCM of 20 and 70 = 2 × 2 × 5 × 7 [Incomplete pair(s): 5, 7] ⇒ Least perfect square divisible by each 20 and 70 = LCM(20, 70) × 5 × 7 = 4900 [Square root of 4900 = √4900 = ±70] Therefore, 4900 is the required number.
Which of the following is the LCM of 20 and 70? 15, 45, 140, 11
If the LCM of 70 and 20 is 140, Find its GCF.
Since the LCM of 70 and 20 = 140
⇒ 140 × GCF(70, 20) = 1400
Therefore, the GCF (greatest common factor) = 1400/140 = 10.
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