BNU1501October/November 20238[1] 60s3t3[2] 30st[3] 30s2t2[4] 60s2t2Question 7b [4]Determine the lowest common multiple (LCM) of the following three terms: 2p2 ,6pq4 ,4p
Question
BNU1501October/November 20238[1] 60s3t3[2] 30st[3] 30s2t2[4] 60s2t2Question 7b [4]Determine the lowest common multiple (LCM) of the following three terms: 2p2 ,6pq4 ,4p
Solution
To find the lowest common multiple (LCM) of the terms 2p², 6pq⁴, and 4p, you need to find the highest power of each factor in the terms.
Step 1: Break down each term into its prime factors.
2p² = 2 * p * p 6pq⁴ = 2 * 3 * p * q * q * q * q 4p = 2 * 2 * p
Step 2: Identify the highest power of each factor across all terms.
The highest power of 2 is 2 (from the term 4p). The highest power of 3 is 1 (from the term 6pq⁴). The highest power of p is 2 (from the term 2p²). The highest power of q is 4 (from the term 6pq⁴).
Step 3: Multiply these highest powers together to get the LCM.
LCM = 2² * 3¹ * p² * q⁴ = 4 * 3 * p² * q⁴ = 12p²q⁴
So, the lowest common multiple (LCM) of the terms 2p², 6pq⁴, and 4p is 12p²q⁴.
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