Least Common Multiple (LCM) of 106 and 151
The least common multiple (LCM) of 106 and 151 is 16006.
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 106 and 151?
First, calculate the GCD of 106 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 151 = 0 remainder 106 |
| 2 | 151 ÷ 106 = 1 remainder 45 |
| 3 | 106 ÷ 45 = 2 remainder 16 |
| 4 | 45 ÷ 16 = 2 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 47 | 8037 |
| 164 and 36 | 1476 |
| 109 and 101 | 11009 |
| 151 and 114 | 17214 |
| 82 and 142 | 5822 |