What is the least common multiple of 21 and 35?

To find the least common multiple (LCM) of 21 and 35, we can use the following steps:

Step 1: Find the prime factorization of each number.

• Prime factorization of 21: 3 × 7
• Prime factorization of 35: 5 × 7

Step 2: Write down the factors of each number, including repeats.

• Factors of 21: 3, 7, 3 × 7
• Factors of 35: 5, 7, 5 × 7

Step 3: Write down the unique factors from both lists.

• Unique factors: 3, 5, 7, 3 × 7, 5 × 7

Step 4: Multiply the unique factors together to find the LCM.

• LCM = 3 × 5 × 7 = 105

Therefore, the least common multiple of 21 and 35 is 105.