LCM of 70, 105 and 175 is 1050. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 70, 105, and 175 is the smallest number among all common multiples of 70, 105, and 175. The first few multiples of 70, 105, and 175 are (70, 140, 210, 280, 350 . . .), (105, 210, 315, 420, 525 . . .), and (175, 350, 525, 700, 875 . . .) 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 70, 105 and 175?
The answer to this question is 1050. The LCM of 70, 105 and 175 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 70, 105 and 175, is the smallest positive integer 1050 which is divisible by both 70, 105 and 175 with no remainder.
How to Find LCM of 70, 105 and 175?
LCM of 70, 105 and 175 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 70, 105 and 175 Using Prime Factorisation Method
The prime factorisation of 70, 105 and 175, respectively, is given by:
70 = (2 × 5 × 7) = 21 × 51 × 71,
105 = (3 × 5 × 7) = 31 × 51 × 71, and
175 = (5 × 5 × 7) = 52 × 71
LCM (70, 105, 170) = 1050
LCM of 70, 105 and 175 Using Division Method
We’ll divide the numbers (70, 105, 170) by their prime factors to get the LCM of 70, 105 and 175 using the division method (preferably common). The LCM of 70, 105 and 175 is calculated by multiplying these divisors.
| 2 | 70 | 105 | 175 |
| 3 | 35 | 105 | 175 |
| 5 | 35 | 35 | 175 |
| 5 | 7 | 7 | 35 |
| 7 | 7 | 7 | 7 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (70, 105, 170) = 1050
LCM of 70, 105 and 175 Using Listing the Multiples
To calculate the LCM of 70, 105 and 175 by listing out the common multiples, list the multiples as shown below
| Multiples of 70 | Multiples of 105 | Multiples of 175 |
| 70 | 105 | 175 |
| 140 | 210 | 350 |
| 210 | 315 | 525 |
| ……….. | …….. | ……. |
| 1050 | 1050 | 1050 |
The smallest common multiple of 70, 105 and 175 is 72.
Therefore LCM (70, 105, 170) = 1050
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LCM of 70, 105 and 175 Solved Example
Question: Find the smallest number that is divisible by 70, 105, 175 exactly.
Solution:
The smallest number that is divisible by 70, 105, and 175 exactly is their LCM.
⇒ Multiples of 70, 105, and 175:
Multiples of 70 = 70, 140, 210, 280, 350, 420, 490, 560, 630, 700, 770, 840, 910, 980, 1050, . . . .
Multiples of 105 = 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, . . . .
Multiples of 175 = 175, 350, 525, 700, 875, 1050, . . . .
Therefore, the LCM of 70, 105, and 175 is 1050.
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