Least Common Multiple (LCM) of 109 and 151
The least common multiple (LCM) of 109 and 151 is 16459.
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 151?
First, calculate the GCD of 109 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 151 = 0 remainder 109 |
| 2 | 151 ÷ 109 = 1 remainder 42 |
| 3 | 109 ÷ 42 = 2 remainder 25 |
| 4 | 42 ÷ 25 = 1 remainder 17 |
| 5 | 25 ÷ 17 = 1 remainder 8 |
| 6 | 17 ÷ 8 = 2 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 103 | 6283 |
| 176 and 113 | 19888 |
| 42 and 77 | 462 |
| 152 and 125 | 19000 |
| 159 and 149 | 23691 |