What is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10? Class 7

What is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10? Class 7

Question 1.

What is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10? Do you remember the answer from Grade 6, Chapter 5? Class 7

Solution:

360; yes.

Question 2.

Here is a problem posed by the ancient Indian Mathematician Mahaviracharya (850 C.E.). Add together [latex]\frac {8}{15}[/latex], [latex]\frac {1}{20}[/latex], [latex]\frac {7}{36}[/latex], [latex]\frac {11}{63}[/latex] and [latex]\frac {1}{21}[/latex]. What do you get? How can we find this sum efficiently? Class 7

Solution:

[latex]\frac {8}{15}[/latex], [latex]\frac {1}{20}[/latex], [latex]\frac {7}{36}[/latex], [latex]\frac {11}{63}[/latex] and [latex]\frac {1}{21}[/latex]

= [latex]\frac {32}{60}[/latex], [latex]\frac {3}{60}[/latex], [latex]\frac {7}{36}[/latex], [latex]\frac {11}{63}[/latex] and [latex]\frac {3}{63}[/latex]

= [latex]\frac {35}{60}[/latex] + [latex]\frac {7}{36}[/latex] + [latex]\frac {14}{63}[/latex]

= [latex]\frac {350}{360}[/latex] + [latex]\frac {70}{360}[/latex] + [latex]\frac {14}{63}[/latex]

= [latex]\frac {420}{360}[/latex] + [latex]\frac {14}{63}[/latex] = [latex]\frac {42}{36}[/latex] + [latex]\frac {14}{63}[/latex]

= [latex]\frac{28 \times 63+14 \times 36}{36 \times 63}[/latex]

= [latex]\frac {7}{6}[/latex] + [latex]\frac {2}{9}[/latex]

= [latex]\frac {21+4}{18}[/latex]

= [latex]\frac {25}{18}[/latex]