Least Common Multiple (LCM) of 84 and 136
The least common multiple (LCM) of 84 and 136 is 2856.
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 84 and 136?
First, calculate the GCD of 84 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 136 = 0 remainder 84 |
| 2 | 136 ÷ 84 = 1 remainder 52 |
| 3 | 84 ÷ 52 = 1 remainder 32 |
| 4 | 52 ÷ 32 = 1 remainder 20 |
| 5 | 32 ÷ 20 = 1 remainder 12 |
| 6 | 20 ÷ 12 = 1 remainder 8 |
| 7 | 12 ÷ 8 = 1 remainder 4 |
| 8 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 146 | 7154 |
| 161 and 10 | 1610 |
| 188 and 108 | 5076 |
| 26 and 175 | 4550 |
| 106 and 103 | 10918 |