How to find LCM between several numbers? For example, how to find LCM between the numbers 7, 24, 3 and 10?
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3Take the lcm of the first two. Take the lcm of that with the third number, etc. – Angina Seng Oct 28 '18 at 08:37
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Welcome to MSE! If the lcm between two numbers $a$ and $b$ is denoted by $[a,b]$, then for three numbers $a,b,c$, $[a,b,c]=[[a,b],c]$, and so on.
Wuestenfux
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Definition: The least common multiple LCM of two or more numbers is the least number which is divisible by each of them without remainder.
For finding LCM, prime factorization might help! The lcm will be the product of multiplying the highest power of each prime number together.
$$7=7\\24=3 \times 2^3 \\3=3\\10=2 \times 5$$
So $$\text{lcm}\{7,24,3,10\}=7 \times 2^3 \times3 \times 5=840$$
Chinnapparaj R
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$$LCM(a,b)=\frac {a\cdot b}{GCD(a,b)}$$ But, $$LCM(a,b,c)\neq\frac {a\cdot b \cdot c}{GCD(a,b,c)}$$ So, the best way is to take partial LCMs, until you reach the last number, following an algorithm: $$LCM(a,b,c,...)=LCM (LCM(a,b),c,...)$$
For $7,24,3$ and $10$:
Select any $2$ numbers randomly (or the way you feel it will be easier) $$LCM(7,3)=21$$ $$LCM(21,10)=210$$
$$LCM(24,210)=\frac {24 \cdot 210}{GCD(24,210)}$$ $$=\frac{24\cdot 210}{6}$$
$$LCM(3,7,10,24)=840$$
pooja somani
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$$LCM(a,b,c)=\frac{a\cdot b\cdot c\cdot GCD(a,b,c)}{GCD(a,b)\cdot GCD(a,c)\cdot GCD(b,c)}$$ – bof Oct 28 '18 at 08:57
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https://math.stackexchange.com/questions/319297/gcd-to-lcm-of-multiple-numbers/1213619#1213619 – bof Oct 28 '18 at 09:01