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Class 10 Maths11)\(LCM \ of \ (2^3 × 3 × 5) \ and \ (2^4 × 5 × 7) \ is\)
1680
LCM = Product of greatest power of each prime factor involved in the numbers
\(= 2^4 × 3 × 5 × 7
= 16 × 3 × 5 × 7
= 1680\)
Class 10 Maths12)A rational number can be expressed as a terminating decimal if the denominator has the factors
2 or 5 only
A rational number can be expressed as a terminating decimal if the denominator has the factors 2 or 5 or both. Any other factors in the denominator yield a non-terminating decimal expansion.
13)An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
8
HCF is the highest number that can be divided exactly into each of two or more numbers. In other words, the HCF of two numbers is the highest number (maximum) that divides both numbers.
Thus, we have the find the HCF of the members in the army band and the army contingent.
HCF (616, 32) will give the maximum number of columns in which they can march. We use Elucid's algorithim to find the H.C.F:
616 = (32 × 19) + 8
32 = (8 × 4) + 0
The HCF (616, 32) is 8.
Therefore, the maximum number of columns in which they can march is 8.