Find the Least Common Multiple of 21 and 84. PAR6.2
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1 point
21
168
84
7
The least common multiple (LCM) of 21 and 84 is 84.
To find the least common multiple (LCM) of 21 and 84, we can use the prime factorization method.
Step 1: Prime factorize each number.
21 = 3 * 7
84 = 2^2 * 3 * 7
Step 2: Write down the highest power of each prime factor.
2^2 * 3 * 7
Step 3: Multiply all the prime factors together.
2^2 * 3 * 7 = 84
Therefore, the least common multiple of 21 and 84 is 84.
To find the Least Common Multiple (LCM) of two numbers, you can use a method called prime factorization. Here's how you can find the LCM of 21 and 84:
Step 1: Find the prime factorization of each number.
- The prime factorization of 21 is 3 x 7.
- The prime factorization of 84 is 2 x 2 x 3 x 7.
Step 2: Identify the common prime factors.
- Both numbers have a prime factor of 3 and 7.
Step 3: Multiply the highest power of each common prime factor.
- The highest power of 3 is 3.
- The highest power of 7 is 7.
Step 4: Multiply the highest powers of the common prime factors together.
- LCM = 3 x 7 = 21.
So, the LCM of 21 and 84 is 21. Therefore, the correct answer is 21.
A soccer coach has 54 jerseys, of which 24 are blue and 30 are red. He wants to sort the jerseys so that each group has both colors of jersey. The coach also wants each group to have an equal number of blue jerseys and an equal number of red jerseys. Which answer best shows how the coach should sort the jerseys using the GCF and the Distributive Property of multiplication over addition? PAR 6.5
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1 point
3(27+12)
6(9 x 4)
2(27 + 12)
6(9 + 4)