Least Common Multiple (LCM) of 109 and 51
The least common multiple (LCM) of 109 and 51 is 5559.
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 109 and 51?
First, calculate the GCD of 109 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 51 = 2 remainder 7 |
| 2 | 51 ÷ 7 = 7 remainder 2 |
| 3 | 7 ÷ 2 = 3 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 133 | 4921 |
| 165 and 149 | 24585 |
| 152 and 130 | 9880 |
| 128 and 10 | 640 |
| 23 and 167 | 3841 |