Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?
Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can cover the distance in complete steps?
Answer:
Step measure of 1
st
Boy=63cm
Step measure of 2
nd
Boy=70cm
Step measure of 3
rd
Boy=77cm
LCM of 63,70,77
LCM=2×3×3×5×7×11=6930
Hence, the minimum distance each should cover so that all can cover the distance in complete steps is 6930 cm.
2 ∣
63,70,77
3 ∣
63,35,77
3 ∣
21,35,77
5 ∣
7,35,77
7 ∣
7,7,77
11 ∣
1,1,11
1,1,1
Step-by-step explanation:
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Answer:
6930 cm
Step-by-step explanation:
To find the minimum distance that all three boys can cover in complete steps, we need to find the least common multiple (LCM) of their step lengths.
The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder.
The step lengths of the three boys are 63 cm, 70 cm, and 77 cm.
To find the LCM of 63, 70 and 77, first find the prime factorization of each number.
Prime factorization is the process of expressing a positive integer as a product of its prime factors.
Prime factorization of 63: 3 × 3 × 7 = 3² × 7
Prime factorization of 70: 2 × 5 × 7
Prime factorization of 77: 7 × 11
To find the LCM, take the highest power of each prime factor that appears in any of the numbers and multiply them together:
[tex]\begin{aligned} \implies \sf LCM &= 2 \times 3^2 \times 5 \times7 \times11 \\&= 2 \times 9 \times 5 \times 7 \times11 \\&= 18 \times 5 \times 7 \times11 \\&= 90 \times 7 \times11 \\&= 630 \times11 \\&=6930\end{aligned}[/tex]
Therefore, the minimum distance each boy should cover so that all can cover the distance in complete steps is 6930 cm.
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