Least Common Multiple (LCM) of 100 and 156
The least common multiple (LCM) of 100 and 156 is 3900.
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 100 and 156?
First, calculate the GCD of 100 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 156 = 0 remainder 100 |
| 2 | 156 ÷ 100 = 1 remainder 56 |
| 3 | 100 ÷ 56 = 1 remainder 44 |
| 4 | 56 ÷ 44 = 1 remainder 12 |
| 5 | 44 ÷ 12 = 3 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 130 | 390 |
| 197 and 104 | 20488 |
| 181 and 137 | 24797 |
| 188 and 36 | 1692 |
| 67 and 86 | 5762 |