Proposition VII.34 — Given two numbers, to find the least number which they measu…

Proof

lcm (a, b) = ab / g cd (a, b)

: multiply

a

b

then divide by the gcd (VII.2).

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Depends on (2)

VII.2Proposition VII.2Given two numbers not prime to one another, to find their greatest common measure.
VII.20Proposition VII.20The least numbers of those which have the same ratio with them measure those which have the same ratio the same number…

Required by (dependents) (5)

VII.35Proposition VII.35If two numbers measure any number, the least number measured by them will also measure the same.
VII.36Proposition VII.36Given three numbers, to find the least number which they measure.
VII.39Proposition VII.39To find the number which is the least that will have given parts.
IX.14Proposition IX.14If a number be the least that is measured by prime numbers, it will not be measured by any other prime number except…
IX.36Proposition IX.36If as many numbers as we please beginning from a unit be set out continuously in double proportion, until the sum of…

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