Least Common Multiple (LCM) of 74 and 189
The least common multiple (LCM) of 74 and 189 is 13986.
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 74 and 189?
First, calculate the GCD of 74 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 189 = 0 remainder 74 |
| 2 | 189 ÷ 74 = 2 remainder 41 |
| 3 | 74 ÷ 41 = 1 remainder 33 |
| 4 | 41 ÷ 33 = 1 remainder 8 |
| 5 | 33 ÷ 8 = 4 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 85 | 340 |
| 100 and 37 | 3700 |
| 191 and 164 | 31324 |
| 178 and 60 | 5340 |
| 174 and 121 | 21054 |