Least Common Multiple (LCM) of 70 and 199
The least common multiple (LCM) of 70 and 199 is 13930.
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 199?
First, calculate the GCD of 70 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 199 = 0 remainder 70 |
| 2 | 199 ÷ 70 = 2 remainder 59 |
| 3 | 70 ÷ 59 = 1 remainder 11 |
| 4 | 59 ÷ 11 = 5 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 37 | 2775 |
| 60 and 81 | 1620 |
| 61 and 66 | 4026 |
| 110 and 118 | 6490 |
| 40 and 97 | 3880 |