Least Common Multiple (LCM) of 101 and 156
The least common multiple (LCM) of 101 and 156 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 101 and 156?
First, calculate the GCD of 101 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 156 = 0 remainder 101 |
| 2 | 156 ÷ 101 = 1 remainder 55 |
| 3 | 101 ÷ 55 = 1 remainder 46 |
| 4 | 55 ÷ 46 = 1 remainder 9 |
| 5 | 46 ÷ 9 = 5 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 33 | 792 |
| 128 and 112 | 896 |
| 117 and 119 | 13923 |
| 181 and 127 | 22987 |
| 120 and 189 | 7560 |