Least Common Multiple (LCM) of 199 and 74
The least common multiple (LCM) of 199 and 74 is 14726.
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 74?
First, calculate the GCD of 199 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 74 = 2 remainder 51 |
| 2 | 74 ÷ 51 = 1 remainder 23 |
| 3 | 51 ÷ 23 = 2 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 178 | 8900 |
| 148 and 65 | 9620 |
| 45 and 107 | 4815 |
| 97 and 139 | 13483 |
| 119 and 184 | 21896 |