MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Worksheets
Tests
Algebra
Geometry
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 20
3 Grade
Addition and Subtraction within 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
Addition, Multiplication, Division
4 Grade
Adding and Subtracting
Addition, Multiplication, Division
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
Expressions
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Expressions
Polynomials
Polynomial Vocabulary
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Inequalities
Linear Functions
8 Grade
Congurence of Triangles
Linear Functions
Systems of equations
Slope
Parametric Linear Equations
Word Problems
Exponents
Roots
Quadratic Equations
Quadratic Inequalities
Rational Inequalities
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Logarithmic Equations
Logarithmic Inequalities
Irrational Equations
Irrational Inequalities
Trigonometry
Trigonometry
Identities
Trigonometry
Trigonometric Equations
Trigonometric Inequalities
Extremal value problems
Numbers Classification
Geometry
Slope
Intercept Theorem
Law of Sines
Law of Cosines
Vectors
Modulus Inequalities
Exponential Inequalities
Exponential Equations
Modulus equations
Probabilities
Functions
Min, Max Values
Limits
Limits of Functions
Monotonicity of Functions
Properties of Triangles
Pythagorean Theorem
Matrices
Complex Numbers
Inverse Trigonometric Functions
Analytic Geometry
Analytic Geometry
Circle
Parabola
Ellipse
Conic sections
Polar coordinates
Derivatives
Derivatives
Applications of Derivatives
Derivatives
Integrals
Integrals
Integration by Parts
Trigonometric Substitutions
Application
Differential Equations
Home
Practice
Least Common Multiple - LCM
Easy
Normal
Difficult
Least Common Multiple - LCM: Problems with Solutions
Problem 1 sent by Maya
Find the least common multiple of 2 and 4.
Solution:
4 = 2 * 2.
4:2 = 2
4:4 = 1
So LCM of 2 and 4 is 4.
Problem 2
Find the least common multiple of 6 and 3.
Solution:
Since
6=3.2
, then
6|3
, so
LCM(6;3)=6
.
Problem 3
Find the least common multiple of 12 and 9.
Solution:
By definition, LCM(12;9) is the smallest number, which divides both 12 and 9. If we factorize them, we see that [tex]12=2^2.3[/tex] and [tex]9=3^2[/tex]. So, if
x
is the LCM of 12 and 9, then [tex]x|3^2[/tex],
x|3
and [tex]x|2^2[/tex].
x|3
follows from [tex]x|3^2[/tex], so we are left with [tex]x|3^2[/tex] and [tex]x|2^2[/tex]. Since [tex]3^2[/tex] and [tex]2^2[/tex] are coprime, [tex]x=2^2\cdot3^2=4\cdot9=36[/tex].
Problem 4
Determine the least common multiple of 7 and 3.
Solution:
Both 7 and 3 are prime, so they are also coprime. Then their LCM is their product, 21.
Problem 5
If
x
is the least common multiple of 8 and 9, find
x
.
Solution:
By factoring both numbers, we see that [tex]8=2^3[/tex], and that [tex]9=3^2[/tex]. They have no common prime factors, so they are coprime. Therefore their least common multiple is their product, 72.
Problem 6
Find the least common multiple of 7 and 12.
Solution:
We see that 7 is a prime number and is therefore coprime with any number, which is not divisible by 7. 7 does not divide 12, so 7 and 12 are coprime numbers. Therefore their LCM is their product, 84.
Problem 7
Find the least common multiple of
15
and
5
.
Solution:
Since
15=5 × 3
, the LCM of
15
and
5
is
15
.
Problem 8
Find the least common multiple of
4
and
10
.
Solution:
The first few multiples of 4 are 4,8,12,16,20,24,... and the first few multiples of 10 are 10,20,30,... The least number to appear in both sequences is 20, so it is the LCM of 4 and 10.
Problem 9
Find the least common multiple of 3 and 9.
Solution:
Since
9=3 × 3
, the LCM of 9 and 3 is 9.
Problem 10
Find the least common multiple of
15
and
6
.
Solution:
[tex]LCM(15;6)=LCM(3.5;3.2)=3.LCM(5;2)=3.5.2=30[/tex]
Problem 11
Find the least common multiple of
14
and
10
.
Solution:
[tex]LCM(14;10)=LCM(2.7;2.5)=2.LCM(7;5)=2.7.5=2.35=70[/tex]
Easy
Normal
Difficult
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Feedback
Contact email:
Follow us on
Twitter
Facebook
Author
Copyright © 2005 - 2024.