1. **State the problem:** We have two numbers, 27 and 36, and we want to show that their least common multiple (LCM) is 108 by grouping blocks in tables of 108 blocks. 2. **Recall the formula for LCM:** The LCM of two numbers $a$ and $b$ can be found using their greatest common divisor (GCD) as: $$\text{LCM}(a,b) = \frac{|a \times b|}{\text{GCD}(a,b)}$$ 3. **Find the GCD of 27 and 36:** - Prime factors of 27: $3^3$ - Prime factors of 36: $2^2 \times 3^2$ - Common prime factors: $3^2 = 9$ So, $\text{GCD}(27,36) = 9$ 4. **Calculate the LCM:** $$\text{LCM}(27,36) = \frac{27 \times 36}{9} = \frac{972}{9} = 108$$ 5. **Explain the grouping:** - The first table has 108 blocks arranged in a 9 by 12 grid. - Grouping in sets of 27 means dividing 108 into 4 groups (since $108 \div 27 = 4$). - Grouping in sets of 36 means dividing 108 into 3 groups (since $108 \div 36 = 3$). 6. **Conclusion:** Since 108 is divisible by both 27 and 36, it is a common multiple. It is the smallest such number, so 108 is the LCM of 27 and 36. This grouping visually demonstrates the LCM concept by showing equal groups of 27 and 36 blocks fitting perfectly into 108 blocks.