A couple simple methods of scaling a UIView transform to fit inside another UIView.

ScaleView.m

/*
/ usage:
/ UIView * myView = [[UIView alloc] initWithFrame:CGRectMake(0, 0, 375, 375)];
/ UIView * myContainer = [[UIView alloc] initWithFrame:CGRectMake(0, 0, 60, 60)];
/ CGFloat scale = [self scaleForSize:myView.bounds.size fitToSize:myContainer.bounds.size];
/ myView.transform = CGAffineTransformScale(CGAffineTransformIdentity, scale, scale);
/ [myContainer addSubview:myView];
*/

- (CGFloat)scaleForSize:(CGSize)source fitToSize:(CGSize)destination {
	CGFloat scale = 1;
	
	scale = (destination.width / source.width);
	
	if (source.height * scale > destination.height) {
		scale = destination.height / source.height;
	}
	
	return scale;
}

/*
/ usage:
/ UIView * myView = [[UIView alloc] initWithFrame:CGRectMake(0, 0, 375, 375)];
/ UIView * myContainer = [[UIView alloc] initWithFrame:CGRectMake(0, 0, 60, 60)];
/ myContainer = [self scaleView:myView toFitInView:myContainer];
/ [myContainer addSubview:myView];
*/

- (UIView *)scaleView:(UIView *)source toFitInView:(UIView *)destination {
	CGFloat scale = 1;
	scale = (destination.bounds.size.width / source.bounds.size.width);
	
	if (source.bounds.size.height * scale > destination.bounds.size.height) {
		scale = destination.bounds.size.height / source.bounds.size.height;
	}
	
	source.transform = CGAffineTransformScale(CGAffineTransformIdentity, scale, scale);
	
	return source;
}

/*
/ usage:
/ UIView * myView = [[UIView alloc] initWithFrame:CGRectMake(0, 0, 375, 375)];
/ UIView * myContainer = [[UIView alloc] initWithFrame:CGRectMake(0, 0, 60, 60)];
/ [self addScaledSubview:myView toView:myContainer];
*/

- (void)addScaledSubview:(UIView *)source toView:(UIView *)destination {
	CGFloat scale = 1;
	scale = (destination.bounds.size.width / source.bounds.size.width);
	
	if (source.bounds.size.height * scale > destination.bounds.size.height) {
		scale = destination.bounds.size.height / source.bounds.size.height;
	}
	
	source.transform = CGAffineTransformScale(CGAffineTransformIdentity, scale, scale);
	
	[destination addSubview:source];
}