Least Common Multiple (LCM) of 199 and 70
The least common multiple (LCM) of 199 and 70 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 199 and 70?
First, calculate the GCD of 199 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 70 = 2 remainder 59 |
| 2 | 70 ÷ 59 = 1 remainder 11 |
| 3 | 59 ÷ 11 = 5 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 14 | 98 |
| 187 and 56 | 10472 |
| 199 and 111 | 22089 |
| 58 and 178 | 5162 |
| 11 and 121 | 121 |