Least Common Multiple (LCM) of 110 and 137
The least common multiple (LCM) of 110 and 137 is 15070.
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 110 and 137?
First, calculate the GCD of 110 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 137 = 0 remainder 110 |
| 2 | 137 ÷ 110 = 1 remainder 27 |
| 3 | 110 ÷ 27 = 4 remainder 2 |
| 4 | 27 ÷ 2 = 13 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 34 | 1020 |
| 64 and 55 | 3520 |
| 133 and 178 | 23674 |
| 24 and 152 | 456 |
| 112 and 134 | 7504 |