LCM of 42 and 70 is 210. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 42 and 70 is the smallest number among all common multiples of 42 and 70. The first few multiples of 42 and 70 are (42, 84, 126, 168, 210, 252, 294, . . . ) 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 42 and 70?
The answer to this question is 210. The LCM of 42 and 70 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 42 and 70, is the smallest positive integer 210 which is divisible by both 42 and 70 with no remainder.
How to Find LCM of 42 and 70?
LCM of 42 and 70 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 42 and 70 Using Prime Factorisation Method
The prime factorisation of 42 and 70, respectively, is given by:
42 = (2 × 3 × 7) = 21 × 31 × 71 and
70 = (2 × 5 × 7) = 21 × 51 × 71
LCM (42, 70) = 210
LCM of 42 and 70 Using Division Method
We’ll divide the numbers (42, 70) by their prime factors to get the LCM of 42 and 70 using the division method (preferably common). The LCM of 42 and 70 is calculated by multiplying these divisors.
| 2 | 42 | 70 |
| 3 | 21 | 35 |
| 3 | 7 | 15 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, (42, 70) = 210
LCM of 42 and 70 Using Listing the Multiples
To calculate the LCM of 42 and 70 by listing out the common multiples, list the multiples as shown below
| Multiples of 42 | Multiples of 70 |
| 42 | 70 |
| 84 | 140 |
| 126 | 210 |
| 168 | 280 |
| 210 | 350 |
The smallest common multiple of 42 and 70 is 210.
Therefore (42, 70) = 210
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LCM of 42 and 70 Solved Examples
Verify the relationship between GCF and LCM of 42 and 70.
Solution:
The relation between GCF and LCM of 42 and 70 is given as,
LCM(42, 70) × GCF(42, 70) = Product of 42, 70
Prime factorization of 42 and 70 is given as, 42 = (2 × 3 × 7) = 21 × 31 × 71 and 70 = (2 × 5 × 7) = 21 × 51 × 71
LCM(42, 70) = 210
GCF(42, 70) = 14
LHS = LCM(42, 70) × GCF(42, 70) = 210 × 14 = 2940
RHS = Product of 42, 70 = 42 × 70 = 2940
⇒ LHS = RHS = 2940
Hence, verified.
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