Find all the pairs of three digit numbers whose lcm is 2400
Answers
Answer:
4800
Step-by-step explanation:
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Answer:
(480, 100), (160, 300), (480, 300), (800, 300), (480, 600), (800, 480)
Step-by-step explanation:
What are all of the pairs of 3 digit numbers whose LCM is 2,400?
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Prime factors of 2400 are (25)∗(31)∗(52)
Underlying numbers can be formed with the following combinations:
Power of 2: Combinations allowed (max: 5) = 6 = {0, 1, 2, 3, 4, 5}
Power of 3: Combinations allowed (max: 1) = 2 = {0, 1}
Power of 5: Combinations allowed (max: 2) = 3 = {0, 1, 2}
Total combinations possible = 6*2*3 = 36
We are interested only in 3 digit numbers and the 11 possible values are:
100,120,150,160,200,240,300,400,480,600,800−−(A)
15 distinct combinations to form a pair of distinct numbers with LCM = 2400 are: (with some manual computations).
(100, 480)
(120, 800)
(150, 160)
(150, 480)
(150, 800)
(200, 480)
(240, 800)
(300, 160)
(300, 480)
(300, 800)
(400, 480)
(600, 160)
(600, 480)
(600, 800)
(800, 480)
One can also try to find the number of combinations possible for each of the 11 numbers provided in (A) and combine them with the respective power of 2, 3 and 5. The constraint to be applied : powers of 2 must add to 6, powers of 3 = 1 and powers of 5 = 2