Least Common Multiple (LCM) of 199 and 79
The least common multiple (LCM) of 199 and 79 is 15721.
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 79?
First, calculate the GCD of 199 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 79 = 2 remainder 41 |
| 2 | 79 ÷ 41 = 1 remainder 38 |
| 3 | 41 ÷ 38 = 1 remainder 3 |
| 4 | 38 ÷ 3 = 12 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 141 | 20022 |
| 160 and 12 | 480 |
| 131 and 35 | 4585 |
| 68 and 154 | 5236 |
| 112 and 88 | 1232 |