Least Common Multiple (LCM) of 148 and 189
The least common multiple (LCM) of 148 and 189 is 27972.
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 148 and 189?
First, calculate the GCD of 148 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 148 ÷ 189 = 0 remainder 148 |
| 2 | 189 ÷ 148 = 1 remainder 41 |
| 3 | 148 ÷ 41 = 3 remainder 25 |
| 4 | 41 ÷ 25 = 1 remainder 16 |
| 5 | 25 ÷ 16 = 1 remainder 9 |
| 6 | 16 ÷ 9 = 1 remainder 7 |
| 7 | 9 ÷ 7 = 1 remainder 2 |
| 8 | 7 ÷ 2 = 3 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 39 | 4134 |
| 145 and 69 | 10005 |
| 123 and 118 | 14514 |
| 167 and 20 | 3340 |
| 158 and 33 | 5214 |