Least Common Multiple (LCM) of 145 and 187
The least common multiple (LCM) of 145 and 187 is 27115.
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 145 and 187?
First, calculate the GCD of 145 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 187 = 0 remainder 145 |
| 2 | 187 ÷ 145 = 1 remainder 42 |
| 3 | 145 ÷ 42 = 3 remainder 19 |
| 4 | 42 ÷ 19 = 2 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 70 | 210 |
| 112 and 81 | 9072 |
| 180 and 73 | 13140 |
| 109 and 56 | 6104 |
| 101 and 158 | 15958 |