Least Common Multiple (LCM) of 110 and 64
The least common multiple (LCM) of 110 and 64 is 3520.
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 64?
First, calculate the GCD of 110 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 64 = 1 remainder 46 |
| 2 | 64 ÷ 46 = 1 remainder 18 |
| 3 | 46 ÷ 18 = 2 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 38 | 152 |
| 131 and 116 | 15196 |
| 113 and 70 | 7910 |
| 171 and 31 | 5301 |
| 67 and 132 | 8844 |