Least Common Multiple (LCM) of 56 and 148
The least common multiple (LCM) of 56 and 148 is 2072.
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 56 and 148?
First, calculate the GCD of 56 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 148 = 0 remainder 56 |
| 2 | 148 ÷ 56 = 2 remainder 36 |
| 3 | 56 ÷ 36 = 1 remainder 20 |
| 4 | 36 ÷ 20 = 1 remainder 16 |
| 5 | 20 ÷ 16 = 1 remainder 4 |
| 6 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 187 | 20383 |
| 87 and 167 | 14529 |
| 36 and 135 | 540 |
| 110 and 80 | 880 |
| 128 and 141 | 18048 |