Math, asked by devarsh89, 1 year ago

Three strings of a musical instrument vibrate six, eight and 12 times the second respectively. If all the three begin to vibrate simultaneously, then find the sort is time interval before all three vibrate together again?

Answers

Answered by k1nh1iy1
3

LCM OF 6,8&12 = 24 sec

Answered by sharonr
3

The shortest time interval before all three vibrate together again is 24 seconds

Solution:

Given that,

Three strings of a musical instrument vibrate 6 , 8 and 12 times the second respectively

All the three begin to vibrate simultaneously, then the shortest time interval before all three vibrate together again is least common multiple of 6 , 8 and 12

Find LCM of 6 , 8 and 12

List all prime factors for each number.

Prime Factorization of 6 is:  2 x 3

Prime Factorization of 8 is:  2 x 2 x 2

Prime Factorization of 12 is:  2 x 2 x 3

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 = 24

Thus the shortest time interval before all three vibrate together again is 24 seconds

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