Dan plans to cut a rope into 12 equal pieces and marks points where he needs to cut. Muhammad plans to cut the same rope into 16 equal pieces and marks points where he needs to cut. Then Maya cuts the rope at all the marked points.How many pieces does Maya get?
Question
Dan plans to cut a rope into 12 equal pieces and marks points where he needs to cut. Muhammad plans to cut the same rope into 16 equal pieces and marks points where he needs to cut. Then Maya cuts the rope at all the marked points.How many pieces does Maya get?
Solution
To solve this problem, we need to find the least common multiple (LCM) of 12 and 16 because the LCM will give us the total number of pieces that Maya will get after cutting the rope at all the marked points.
Step 1: Prime factorize the numbers 12 = 2^2 * 3 16 = 2^4
Step 2: Find the LCM The LCM is found by multiplying the highest power of all prime numbers in the factorization. So, LCM = 2^4 * 3 = 48
Therefore, Maya gets 48 pieces after cutting the rope at all the marked points.
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