Number System: Aptitude Questions and Answers-6

Step(1): Factorize the numbers into their prime factors.$$ 3 = 3^{1} $$ $$ 6 = 2^{1} \times 3^{1} $$ $$ 10 = 2^{1} \times 5^{1} $$ Step(2): Collect all the distinct factors with their maximum available power.$$ = 2^{1}, \ 3^{1}, \ 5^{1} $$ Step(3): Multiply the collected factors.$$ = 2 \times 3 \times 5 = 30 $$ Here, 30 is the smallest positive number which is exactly divisible by 3, 6, and 10.

Step(1): Factorize the numbers into their prime factors.$$ 15 = 3 \times 5 = 3^{1} \times 5^{1} $$ $$ 20 = 2 \times 2 \times 5 = 2^{2} \times 5^{1} $$ $$ 27 = 3 \times 3 \times 3 = 3^{3} $$ Step(2): Collect all the distinct factors with their maximum available power.$$ = 2^{2}, \ 3^{3}, \ 5^{1} $$ Step(3): Multiply the collected factors.$$ = 2^{2} \times 3^{3} \times 5^{1} $$ $$ = 4 \times 27 \times 5 = 540 $$ Here, 540 is the smallest positive number which is exactly divisible by 15, 20, and 27.

Step(1): Factorize the numbers into their prime factors.$$ 56 = 2 \times 2 \times 2 \times 7 = 2^{3} \times 7^{1} $$ $$ 78 = 2 \times 3 \times 13 = 2^{1} \times 3^{1} \times 13^{1} $$ $$ 99 = 3 \times 3 \times 11 = 3^{2} \times 11^{1} $$ Step(2): Collect all the distinct factors with their maximum available power.$$ = 2^{3}, \ 3^{2}, \ 7^{1} \ 11^{1} \ 13^{1} $$ Step(3): Multiply the collected factors.$$ = 2^{3} \times 3^{2} \times 7^{1} \times 11^{1} \times 13^{1} $$ $$ = 8 \times 9 \times 7 \times 11 \times 13 = 72072 $$

Step(1): Factorize the numbers into their prime factors.$$ 35 = 5^{1} \times 7^{1} $$ $$ 40 = 2 \times 2 \times 2 \times 5 = 2^{3} \times 5^{1} $$ $$ 50 = 2 \times 5 \times 5 = 2^{1} \times 5^{2} $$ Step(2): Collect all the distinct factors with their maximum available power.$$ = 2^{3}, \ 5^{2}, \ 7^{1} $$ Step(3): Multiply the collected factors.$$ = 2^{3} \times 5^{2} \times 7^{1} $$ $$ = 8 \times 25 \times 7 = 1400 $$