Problems from Greatest common divisor and Least common multiple

Find the greatest common divisor of the following sets of numbers: $(34, 25), (80, 45), (66, 52, 70)$ .

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$34 = 2 \times 17, 25 = 5^{2}$

$g . c . d . (34, 25) = 1$ (They do not have common divisors but $1$ .)

$80 = 2^{4} \times 5, 45 = 3^{2} \times 5$

$g . c . d (80, 45) = 5$

$66 = 2 \times 3 \times 11, 52 = 2^{2} \times 13, 70 = 2 \times 5 \times 6$

$g . c . d . (66, 52, 70) = 2$

$g . c . d . (34, 25) = 1 g . c . d . (80, 45) = 5 g . c . d . (66, 52, 70) = 2$

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Find the least common multiple of the following sets of numbers: $(49, 33), (56, 100, 24), (72, 41, 16)$ .

See development and solution

$49 = 7^{2}, 33 = 3 \times 11$

$l . c . m . (49, 33) = 3 \times 7^{2} \times 11 = 1617$

$56 = 2^{3} \times 7, 100 = 2^{2} \times 5^{2}, 24 = 2^{3} \times 3$

$l . c . m . (56, 100, 24) = 2^{3} \times 3 \times 5^{2} \times 7 = 4200$

$72 = 2^{3} \times 3^{2}, 41 = 41 \times 1, 16 = 2^{4}$

$l . c . m . (72, 41, 16) = 2^{4} \times 3^{2} \times 41 = 5904$

$l . c . m . (49, 39) = 1617 l . c . m . (56, 100, 24) = 4200 l . c . m . (72, 41, 16) = 5904$

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