LCM of 50 and 70 is 350. The LCM of any two integers in math is the value that is evenly divisible by the two values. Among all common multiples of 50 and 70, the LCM of 50 and 70 is the smallest number. (50, 100, 150, 200, 250, 300, 350,..) and (70, 140, 210, 280, 350, 420, 490,..) are the first few multiples of 50 and 70, respectively. The division method, listing multiples, and prime factorization are three commonly used methods for calculating the LCM of 50 and 70.
Also read: Least common multiple
What is LCM of 50 and 70?
The answer to this question is 350. The LCM of 50 and 70 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 50 and 70, is the smallest positive integer 350 which is divisible by both 50 and 70 with no remainder.
How to Find LCM of 50 and 70?
LCM of 50 and 70 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 50 and 70 Using Prime Factorisation Method
The prime factorisation of 50 and 70, respectively, is given by:
50 = (2 × 5 × 5) = 21 × 52 and
70 = (2 × 5 × 7) = 21 × 51 × 71
LCM (50, 70) = 350
LCM of 50 and 70 Using Division Method
We’ll divide the numbers (50, 70) by their prime factors to get the LCM of 50 and 70 using the division method (preferably common). The LCM of 50 and 70 is calculated by multiplying these divisors.
| 2 | 50 | 70 |
| 5 | 25 | 35 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (50, 70) = 350
LCM of 50 and 70 Using Listing the Multiples
To calculate the LCM of 50 and 70 by listing out the common multiples, list the multiples as shown below
| Multiples of 50 | Multiples of 36 |
| 50 | 70 |
| 100 | 140 |
| 150 | 210 |
| 200 | 280 |
| 250 | 350 |
| 300 | 420 |
| 350 | 490 |
The smallest common multiple of 50 and 70 is 350.
Therefore LCM (50, 70) = 350
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LCM of 50 and 70 Solved Example
Question: Find the smallest number that is divisible by 50 and 70 exactly.
Solution:
The smallest number that is divisible by 50 and 70 exactly is their LCM.
⇒ Multiples of 50 and 70:
Multiples of 50 = 50, 100, 150, 200, 250, 300, 350, . . . .
Multiples of 70 = 70, 140, 210, 280, 350, . . . .
Therefore, the LCM of 50 and 70 is 350.
Frequently Asked Questions on LCM of 50 and 70
What is the LCM of 50 and 70?
List the methods used to find the LCM of 50 and 70.
Which of the following is the LCM of 50 and 70? 2, 350, 15, 5.
What is the Least Perfect Square Divisible by 50 and 70?
LCM of 50 and 70 = 2 × 5 × 5 × 7 [Incomplete pair(s): 2, 7] ⇒ Least perfect square divisible by each 50 and 70 = LCM(50, 70) × 2 × 7 = 4900 [Square root of 4900 = √4900 = ±70] Therefore, 4900 is the required number.
If the LCM of 70 and 50 is 350, Find its GCF.
Since the LCM of 70 and 50 = 350
⇒ 350 × GCF(70, 50) = 3500
Therefore, the greatest common factor = 3500/350 = 10.
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