Least Common Multiple (LCM) of 70 and 113
The least common multiple (LCM) of 70 and 113 is 7910.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 70 and 113?
First, calculate the GCD of 70 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 113 = 0 remainder 70 |
| 2 | 113 ÷ 70 = 1 remainder 43 |
| 3 | 70 ÷ 43 = 1 remainder 27 |
| 4 | 43 ÷ 27 = 1 remainder 16 |
| 5 | 27 ÷ 16 = 1 remainder 11 |
| 6 | 16 ÷ 11 = 1 remainder 5 |
| 7 | 11 ÷ 5 = 2 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 96 | 1440 |
| 110 and 166 | 9130 |
| 52 and 105 | 5460 |
| 87 and 198 | 5742 |
| 129 and 145 | 18705 |