Least Common Multiple (LCM) of 55 and 149
The least common multiple (LCM) of 55 and 149 is 8195.
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 55 and 149?
First, calculate the GCD of 55 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 149 = 0 remainder 55 |
| 2 | 149 ÷ 55 = 2 remainder 39 |
| 3 | 55 ÷ 39 = 1 remainder 16 |
| 4 | 39 ÷ 16 = 2 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 27 | 4104 |
| 145 and 199 | 28855 |
| 165 and 32 | 5280 |
| 140 and 98 | 980 |
| 75 and 125 | 375 |