Least Common Multiple (LCM) of 109 and 152
The least common multiple (LCM) of 109 and 152 is 16568.
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 152?
First, calculate the GCD of 109 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 152 = 0 remainder 109 |
| 2 | 152 ÷ 109 = 1 remainder 43 |
| 3 | 109 ÷ 43 = 2 remainder 23 |
| 4 | 43 ÷ 23 = 1 remainder 20 |
| 5 | 23 ÷ 20 = 1 remainder 3 |
| 6 | 20 ÷ 3 = 6 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 167 | 13861 |
| 143 and 100 | 14300 |
| 19 and 84 | 1596 |
| 134 and 50 | 3350 |
| 87 and 165 | 4785 |