Least Common Multiple (LCM) of 107 and 151
The least common multiple (LCM) of 107 and 151 is 16157.
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 107 and 151?
First, calculate the GCD of 107 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 151 = 0 remainder 107 |
| 2 | 151 ÷ 107 = 1 remainder 44 |
| 3 | 107 ÷ 44 = 2 remainder 19 |
| 4 | 44 ÷ 19 = 2 remainder 6 |
| 5 | 19 ÷ 6 = 3 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 85 | 1700 |
| 88 and 122 | 5368 |
| 117 and 149 | 17433 |
| 119 and 135 | 16065 |
| 49 and 126 | 882 |