Least Common Multiple (LCM) of 56 and 149
The least common multiple (LCM) of 56 and 149 is 8344.
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 149?
First, calculate the GCD of 56 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 149 = 0 remainder 56 |
| 2 | 149 ÷ 56 = 2 remainder 37 |
| 3 | 56 ÷ 37 = 1 remainder 19 |
| 4 | 37 ÷ 19 = 1 remainder 18 |
| 5 | 19 ÷ 18 = 1 remainder 1 |
| 6 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 38 | 4978 |
| 157 and 156 | 24492 |
| 113 and 92 | 10396 |
| 112 and 13 | 1456 |
| 18 and 72 | 72 |