If 5A=12B=13C, find A:B:C.
- A60:65:156
- B65:156:60
- C156:65:60
- D13:12:5
Solution & Step-by-step Explanation
Given the equation:
5A=12B=13C
To find the ratio A:B:C, let us find the least common multiple (LCM) of the coefficients 5, 12, and 13. Since 5 and 13 are prime numbers and 12 shares no common factor with them, their LCM is:
LCM(5,12,13)=5×12×13=780
Divide each term by the LCM:
780
5A
=
780
12B
=
780
13C
156
A
=
65
B
=
60
C
Therefore, the ratio is:
A:B:C=156:65:60
5A=12B=13C
To find the ratio A:B:C, let us find the least common multiple (LCM) of the coefficients 5, 12, and 13. Since 5 and 13 are prime numbers and 12 shares no common factor with them, their LCM is:
LCM(5,12,13)=5×12×13=780
Divide each term by the LCM:
780
5A
=
780
12B
=
780
13C
156
A
=
65
B
=
60
C
Therefore, the ratio is:
A:B:C=156:65:60