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Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together?
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Three boys step off together from the same place . If their steps meas...
Understanding the Problem
To find the distance at which the three boys will step together, we need to determine the least common multiple (LCM) of the lengths of their steps: 36 cm, 48 cm, and 54 cm.
Finding the LCM
1. **Prime Factorization**:
- 36 = 2² × 3²
- 48 = 2⁴ × 3¹
- 54 = 2¹ × 3³
2. **Identify Highest Powers**:
- For 2: The highest power is 2⁴ (from 48).
- For 3: The highest power is 3³ (from 54).
3. **Calculate LCM**:
- LCM = 2⁴ × 3³
- Calculate 16 × 27 = 432
Conclusion
The distance from the starting point where all three boys will step together is:
- **432 cm**
Summary
- The boys step off with step lengths of:
- **36 cm**
- **48 cm**
- **54 cm**
- The LCM found is:
- **432 cm**
Thus, they will step together at a distance of **432 cm** from the starting point.
To find the distance at which the three boys will step together, we need to determine the least common multiple (LCM) of the lengths of their steps: 36 cm, 48 cm, and 54 cm.
Finding the LCM
1. **Prime Factorization**:
- 36 = 2² × 3²
- 48 = 2⁴ × 3¹
- 54 = 2¹ × 3³
2. **Identify Highest Powers**:
- For 2: The highest power is 2⁴ (from 48).
- For 3: The highest power is 3³ (from 54).
3. **Calculate LCM**:
- LCM = 2⁴ × 3³
- Calculate 16 × 27 = 432
Conclusion
The distance from the starting point where all three boys will step together is:
- **432 cm**
Summary
- The boys step off with step lengths of:
- **36 cm**
- **48 cm**
- **54 cm**
- The LCM found is:
- **432 cm**
Thus, they will step together at a distance of **432 cm** from the starting point.
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Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together?
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Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together?.
Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three boys step off together from the same place . If their steps measure 36cm,48cm and 54cm, at what distance from the starting point will they step together?.
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