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 |
|---|---|
| 175 and 14 | 350 |
| 199 and 151 | 30049 |
| 110 and 110 | 110 |
| 138 and 121 | 16698 |
| 135 and 16 | 2160 |