Least Common Multiple (LCM) of 48 and 149
The least common multiple (LCM) of 48 and 149 is 7152.
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 48 and 149?
First, calculate the GCD of 48 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 149 = 0 remainder 48 |
| 2 | 149 ÷ 48 = 3 remainder 5 |
| 3 | 48 ÷ 5 = 9 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 77 | 6930 |
| 117 and 155 | 18135 |
| 160 and 187 | 29920 |
| 181 and 29 | 5249 |
| 122 and 71 | 8662 |