Least Common Multiple (LCM) of 109 and 62
The least common multiple (LCM) of 109 and 62 is 6758.
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 62?
First, calculate the GCD of 109 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 62 = 1 remainder 47 |
| 2 | 62 ÷ 47 = 1 remainder 15 |
| 3 | 47 ÷ 15 = 3 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 75 | 2850 |
| 106 and 184 | 9752 |
| 169 and 21 | 3549 |
| 26 and 144 | 1872 |
| 192 and 126 | 4032 |