Least Common Multiple (LCM) of 156 and 101
The least common multiple (LCM) of 156 and 101 is 15756.
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 156 and 101?
First, calculate the GCD of 156 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 101 = 1 remainder 55 |
| 2 | 101 ÷ 55 = 1 remainder 46 |
| 3 | 55 ÷ 46 = 1 remainder 9 |
| 4 | 46 ÷ 9 = 5 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 69 | 10005 |
| 120 and 117 | 4680 |
| 118 and 163 | 19234 |
| 145 and 177 | 25665 |
| 112 and 34 | 1904 |