Least Common Multiple (LCM) of 110 and 49
The least common multiple (LCM) of 110 and 49 is 5390.
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 49?
First, calculate the GCD of 110 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 49 = 2 remainder 12 |
| 2 | 49 ÷ 12 = 4 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 88 | 5368 |
| 10 and 130 | 130 |
| 110 and 45 | 990 |
| 131 and 10 | 1310 |
| 161 and 120 | 19320 |