Let a and b be any two positive integers. Define the least common multiple of a and b to be the integerl = ab gcd (a,b) . Show that,a) a|l and b|l;b) If m is a positive integer such that a|m and b|m, then l|m. 14. Let a and b be any two positive integers. Define the least common multiple of a and b to be theintegerabShow that,gcd (a,b)a) all and bl;b) If m is a positive integer such that a|m and b|m, then l|m.

As per the question we are given the least common multiple of two integers a, b as : l = ab/gcd(a,b)…

Let a and b be any two positive integers. Define the least common multiple of a and b to be the integer ab gcd (a,b) Show that, a) all and bll; b) If m is a positive integer such that alm and blm, then l|m.

Let a and b be any two positive integers. Define the least common multiple of a and b to be the integer ab gcd (a,b) Show that, a) all and bll; b) If m is a positive integer such that alm and blm, then l|m.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let a and b be any two positive integers. Define the least common multiple of a and b to be the integer

l = ab gcd (a,b) . Show that,

a) a|l and b|l;
b) If m is a positive integer such that a|m and b|m, then l|m.

14. Let a and b be any two positive integers. Define the least common multiple of a and b to be the
integer
ab
Show that,
gcd (a,b)
a) all and bl;
b) If m is a positive integer such that a|m and b|m, then l|m.

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